1
A particle moving along the positive x-axis has the following
positions at various times:
x(cm) t(s)
0.089 0.0
0.040 1.0
0.010 2.0
0.050 3.0
0.080 4.0
0.130 5.0
0.020 6.0
(a) Plot a position versus time graph
(b) Plot displacement versus time graph
(c) Find the average velocity of the particle in the intervals 0.0
to 1.0 s, 0.0 to 2.0 s, 0.0 to 3.0 s, 0.0 to 4.0 s
(d) Find the slope of the curve drawn in part a at the points t =
0.0, 1.0, 2.0, 3.0, 4.0, and 5.0 s.
5
Answer
(a) 12.16 m/s
(b) 4.05 m/s
6
Answer
(a) GRAPH
(b) GRAPH
(c) -0.040 m/s
-0.035 m/s
-0.010 m/s
0.0 m/s
(d) -0.040 m/s
-0.20 m/s
0.0 m/s
+0.020 m/s
+0.040 m/s
+0.060 m/s
2
A horse canters away from its trainer in a straight line, moving
150 m away in 14 s. It then turns abruptly and gallops halfway
back in 4.5 s.
(a) Calculate its average speed for the entire trip.
(b) Calculate its average velocity for the entire trip, using
"away from the trainer" as the positive direction.
A mining cart is pulled up a hill at 20 km/h and then pulled
back down the hill at 35 km/h through its original level. (The
time required for the cart's reversal at the top of its climb is
negligible.) What is the average speed of the cart for its round
trip, from its original level back to its original level?
Answer
25 km/h
7
Here are three pairs of initial and final positions, respectively,
along an x axis. Which pairs give a negative displacement: (a)
-3 m, +5 m; (b) -3 m, -7 m; (c) 7 m, -3 m?
A pilot flies horizontally at 1300 km/h, at height h = 35 m
above initially level ground. However, at time t = 0, the pilot
begins to fly over ground sloping upward at angle θ = 4.30 (see
the figure). If the pilot does not change the airplane's heading,
at what time t does the plane strike the ground?
Answer
b and c
3
A bird can fly 25 km/h. How long does it take to fly 18 km?
(give the answers in hours and minutes)
Answer
1.29 s
Answer
.72 hr
43.2 minutes
4
A car travels 40 km up a hill at a constant speed of 40 km/h
and returns down the hill at a constant speed of 60 km/h.
Always moving away from the starting Point
(a) Draw a position time graph of the motion of the car.
(b) Draw a velocity time graph of the motion of the car.
Accurately align the velocity time graph accurately below the
position time graph.
(c) Calculate the average speed for the round trip.
Answer
(a) Picture
(b) Picture
(c) 48 km/h
8
An airplane travels 2400 km at a speed of 800 km/h, and then
encounters a tailwind that boosts its speed to 1000 km/h for the
next 1800 km.
(a) What was the total time for the trip?
(b) What was the average speed of the plane for this trip
Answer
(a) 4.8 hours
(b) 875 km/hr
9
An automobile travels on a straight road for 40 km at 30 km/h.
It then continues in the same direction for another 40 km at 60
km/h.
(a) What is the average velocity of the car during this 80 km
trip'? (Assume that it moves in the positive x direction.)
(b) What is the average speed?
(c) Graph x versus t and indicate how the average velocity is
found on the graph.
Answer
(a) +40 km/h;
(b) 40 km/h
(c) Graph
10
11
Average speed can mean the magnitude of the average velocity
vector. Another meaning given to it is the average speed is the
total length of path traveled divided by the elapse time. Are
these meanings different? If so, give an example.
Answer
Compute your average velocity in the following two cases:
(a) You walk 73.2 m at a speed of 1.22 m/s and then run 73.2
m at a speed of 3.05 m/s along a straight track.
(b) You walk for 1.00 min at a speed of 1.22 m/s and then run
for 1.00 min at 3.05 m/s along a straight track.
(c) Graph x versus t for both cases and indicate how the
average velocity is found on the graph.
The meanings are different. Consider a round trip and
point out that the average speed is zero by the first
definition but non-zero by the second.
Answer
The 1992 world speed record for a bicycle (human powered
vehicle) was set by Chris Huber. His time through the
measured 200 m stretch was a sizzling 6.509 s, at which he
commented, "Cogito ergo zoom!" (I think, therefore I go fast!).
In 2001, Sam Whittingham beat Huber's record by 19.0 km/h.
What was Whittingham's time through the 200 m?
14
(a) 1.74 m/s;
(b) 2.14 m/s
15
During a hard sneeze, your eyes might shut for 0.50 s. If you
are driving a car at 90 km/h during such a sneeze, how far does
the car move during that time? (give answer in meters)
Answer
Answer
12.5 m
5.554 s
12
The figure shows four paths along which objects move from a
starting point to a final point, all in the same time interval. The
paths pass over a grid of equally spaced straight lines.
(a) Rank the paths according to the average velocity of the
objects, greatest first.
(b) Rank the paths according to the average speed of the
objects, greatest first.
16
From January 26, 1977, to September 18, 1983, George
Meegan of Great Britain walked from Ushuaia, at the southern
tip of South America, to Prudhoe Bay in Alaska, covering
30600 km. In meters per second, what was his average speed
during that time period? (give answer in m/s)
Answer
0.146 m/s
17
How far can a cyclist travel in 4.0 h if his average speed is 18
km/h?
Answer
72 km
Answer
18
(a) all tie;
(b) 4, tie of 1 and 2, then 3
13
Calculate the average speed and average velocity of a complete
round trip in which the first 200 km is covered at 90 km/h,
followed by a one-hour lunch break, and the final 200 km is
covered at 50 km/h.
Answer
If a baseball pitcher throws a fastball at a horizontal speed of
160 km/h, how long does the ball take to reach home plate 18.4
m away'?
Answer
.414 s
19
Average Speed
55.40 km/hr
If an accurate speedometer registers a constant value for a
period of time, can you determine the average velocity over
that period of time using only the speedometer? Explain.
Answer
Average Velocity
0
No, the speedometer only gives magnitude not direction.
20
In 1889, at Jubbuipore, India, a tug-of-war was finally won
after 2 h 41 min, with the winning team displacing the center
of the rope 3.7 m. In centimeters per minute, what was the
magnitude of the average velocity of that center point during
the contest?
Answer
2.3 cm/min
21
On average, an eye blink lasts about 100 ms. How far does a
MiG-25 "Foxbat" fighter travel during a pilot's blink if the
plane's average velocity is 3400 km/h?
25
Two locomotives shown in the figure approach each other on
parallel tracks. Each has a speed of 120 km/h with respect to
the ground. If they are initially 8.5 km apart, how long will it
be before they pass each other? (give your answer in seconds)
Answer
94.44 m
22
The picture shows the motion of an armadillo that can scamper
left and right along a straight line. The bottom picture (b)
shows his motion (position & time) on a motion map. The top
picture (a) shows the same motion on a position-time graph.
Use the two pictures to answer the following questions.
(a) When, if ever, is the animal to the left of the origin on the
axis?
(b) When, if ever, is its velocity negative,
(c) When, if ever, is its velocity positive
(d) When, if ever, is its velocity zero?
Answer
.035 hr
127 sec
2.1 minutes
26
What must be your average speed in order to travel 330 km in
4.25 h?
Answer
77.65 km/hr
27
Answer
Book Example
(a) between 0 and 3 sec
(b) never
(c) between 0 and 5 sec
(d) never
23
The sport with the fastest moving ball is jai alai, where
measured speeds have reached 303 km/h. If a professional jai
alai player faces a ball at that speed and involuntarily blinks, he
blacks out the scene for 100 ms. How far does the ball move
during the blackout?
When the legal speed limit for the New York Thruway was
increased from 55 mi/h to 65 mi/h, how much time was saved
by a motorist who drove the 700 km between the Buffalo
entrance and the New York City exit at the legal speed limit?
Answer
1.216 h
1 hr 12.96 seconds
28
You are to drive to an interview in another town, at a distance
of 300 km on an expressway. The interview is at 11:15 A.M.
You plan to drive at 100 km/h, so you leave at 8:00 A.M. to
allow some extra time. You drive at that speed for the first 100
km, but then construction work forces you to slow to 40 km/h
for 40 km. What would be the least speed needed for the rest of
the trip to arrive in time for the interview?
Answer
Answer
8.416 m
24
The wings on a stonefly do not flap, and thus the insect cannot
fly. However, when the insect is on a water surface, it can sail
across the surface by lifting its wings into a breeze. Suppose
that you time stoneflies as they move at constant speed along a
straight path of a certain length. On average, the trips each take
7.1 s with the wings set as sails and 25.0 s with the wings
tucked in.
(a) What is the ratio of the sailing speed vs to the nonsailing
(tucked) speed vt?
(b) In terms of vs what is the difference in the times the insects
take to travel the first 2.0 m along the path with and without
sailing?
Answer
(a) 3.5 to 1
(b) (1.43)/vt
128 km/h
29
You drive a beat-up pickup truck along a straight road for 8.4
km at 70 km/h, at which point the truck runs out of gasoline
and stops. Over the next 30 min, you walk another 2.0 km
farther along the road to a gasoline station.
(a) What is your overall displacement from the beginning of
your drive to your arrival at the station?
(b) What is the time interval ∆t from the beginning of your
drive to your arrival at the station?
(c) What is your average velocity vavg from the beginning of
your drive to your arrival at the station? Find it both
numerically and graphically.
(d) Suppose that to pump the gasoline, pay for it, and walk
back to the truck takes you another 45 min. What is your
average speed from the beginning of your drive to your return
to the truck with the gasoline?
33
What must be your car’s average speed in order to travel 235
km in 3.25 h? (Give the answer in both km/hr and in m/s)
Answer
72.3 km/hr
20.08 m/s
34
A bird can fly 25 km/hr. How long does it take to fly 15 km?
(Give the answer in hours and in minutes)
Answer
.6 hours
36 minutes
Answer
Text Book Example
35
(a) 10.4 km
(b) .62 hr
37.2 minutes
(c) 16.8 km/hr
(d) 9.1 km/hr
A horse canters away from its trainer in a straight line, moving
116 m away in 14.0 s. It then turns abruptly and gallops
halfway back in 4.8 s. (using “away from the trainer” as the
positive direction)
(a) Calculate its average speed for the entire trip.
(b) Calculate its average velocity for the entire trip.
Answer
30
31
You drive a beat-up pickup truck along a straight road for 8.4
km at 70 km/h, at which point the truck runs out of gasoline
and stops. Over the next 30 min, you walk another 2.0 km
farther along the road to a gasoline station. Suppose that to
pump the gasoline, pay for it, and walk back to the truck takes
you another 45 min. Suppose that right after refueling the
truck, you drive back to x, at 35 km/h. What is your average
velocity for your entire trip?
(a) 9.26 m/s
(b) 3.1 m/s
36
Answer
Answer
zero (zero displacement for the entire trip)
6.73 m/s
You drive on Interstate 10 from San Antonio to Houston, half
the time at 55 km/h and the other half at 90 km/h. On the way
back you travel half the distance at 55 km/h and the other half
at 90 km/h.
(a) What is your average speed from San Antonio to Houston?
(b) What is your average speed from Houston back to San
Antonio?
(c) What is your average speed for the entire trip?
(d) What is your average velocity for the entire trip?
(e) Sketch x versus t for (a), assuming the motion is all in the
positive x direction. Indicate how the average velocity can be
found on the sketch.
37
-2.452 cm/s
38
(a) 73 km/h;
(b) 68 km/h;
(c) 70 km/h;
(d) 0
(e) graphing
Can an object have a varying speed if its velocity is constant?
If yes, give examples.
A rolling ball moves from x1 = 3.4 cm to x2 = -4.2 cm during
the time from t1 = 3.0 s to t2 = 6.1 s. What is its average
velocity?
Answer
Answer
32
A bowling ball traveling with constant speed hits the pins at
the end of a bowling lane 16.5 m long. The bowler hears the
sound of the ball hitting the pins 2.50 s after the ball is released
from his hands. What is the speed of the ball? The speed of
sound is 340 m/s.
You are driving home from school steadily at 95 km/hr for 130
km. It then begins to rain and you slow to 65 km/hr. You
arrive home after driving 3 hours and 20 minutes.
(a) How far is your hometown from school?
(b) What was your average speed?
Answer
(a) 257.5 km
(b) 77.3 km/hr
39
A race car driver must average 200 km/hr over the course of a
time trial lasting ten laps. If the first nine laps were done at
198.0 km/h what average speed must be maintained for the last
lap?
Answer
By definition, if an object has a constant velocity, then
both the object’s speed and its direction of motion are
constant. Therefore the object cannot have a varying speed
if its velocity is constant.
Answer
220 km/hr
40
Does a car speedometer measure speed, velocity, or both?
44
The graph of x versus t (see figure to the left) is for a particle in
straight line motion. State for each interval whether the
velocity vx is +, -, or 0.
Answer
Speed
41
Raindrops falling past a mercury-arc lamp at night appear, by a
stroboscope effect, to be "frozen" into a string of stationary
streaks 6 cm apart. At what speed are the raindrops falling?
Note that raindrops, because of air resistance, quickly reach a
constant, terminal, speed. The street lamp operates from a 60
Hz power line, which means that the lamp is at maximum
brightness 120 times each second.
Answer
7.20 m/s
42
Answer
The figure is a graph of a particle's position along an x axis
versus time.
(a) At time t = 0, what is the sign of the particle's position?
(b) Is the particle's velocity positive, negative, or 0 at t = 1 s?
(c) Is the particle's velocity positive, negative, or 0 at t = 2 s?
(d) Is the particle's velocity positive, negative, or 0 at t = 3 s?
(e) How many times does the particle go through the point x =
0?
vx
OA
AB
BC
CD
45
+
0
+
+
When an object moves with constant velocity, does its average
velocity during any time interval differ from its instantaneous
velocity at any instant
Answer
When an object moves with constant velocity, its average
velocity over any time interval is exactly equal to its
instantaneous velocity at all times
46
Answer
(a) negative;
(b) positive;
(c) zero;
(d) negative;
(e) twice
43
The graph of x versus t (see figure to the left) is for a particle in
straight line motion. State for each interval whether the
velocity vx is +, -, or 0.
Answer
(a)
(b)
(c)
(d)
(e)
(f)
47
vx
OA
AB
BC
CD
-6 m/s
decreasing
6 m/s
greater
yes
no
Each second a rabbit moves half the remaining distance from
his nose to a head of lettuce.
(a) Does the rabbit ever get to the lettuce?
(b) What is the limiting value of the rabbit's average velocity.
(c) Draw graphs showing his velocity and position as time
increases.
Answer
Answer
(a)
A particle's position is given by x = 4 - 12t + 3t2 (where t is in
seconds and x is in meters).
(a) What is the particle's velocity at t = 1 s?
(b) Is the particle moving toward increasing or decreasing x
just then?
(c) What is its speed just then?
(d) Is the speed larger or smaller at later times?
Try to answer the next two questions without further
calculations.
(e) Is there ever an instant when the velocity is zero? Explain
(f) Is there a time after t = 3 s when the particle is moving
leftward on the axis? Explain.
+
+
0
-
See physics by Genzer and Young Sliver Burdette for
complete description pg. 35-49 of the linear case similar to
Zeno Experiment.
(a) Theoretically he never reaches the lettuce.
(b) The limiting factor is the distance, because he cannot
go to the lettuce no matter how long he moves half-way.
(c)
48
The coordinates of a particle moving along the x-axis is given
in meters by x = 3.5 t - 5.7 t2, where t is the time in seconds.
(a) Calculate the average velocity for each of the intervals:
0 to 1 s
0 to 0.1 s
0 to 0.01 s
0 to 0.001 s
(b) Using the information from (a) Estimate the particle's
instantaneous velocity at t = 0.
51
Answer
(a) see below
2.2 m/s 0 to 1 s
2.9 m/s 0 to 0.1 s
3.4 m/s 0 to 0.01 s
3.49 m/s 0 to 0.001 s
Answer
(b) 3.50 m/s
49
(a) 0;
(b) 4.0 m;
(c) -0.82 s;
(d) 0.82 s;
(e) see graph
(f) +20t;
(g) increase
The following equations give the position x(t) of a particle in
four situations (in each equation, x is in meters, t is in seconds,
and t > 0):
(1) x = 3t2
(2) x = -4t2 - 2
(3) x = 2/t2
(4) x = -2
52
(a) In which situation is the velocity v of the particle constant?
(b) In which is v in the negative x direction?
Answer
(a) 4
(b) 2 and 3
50
(a) In which situation is the velocity v of the particle constant?
(b) In which situation is v in the negative x direction?
(c) In which situation is the particle slowing?
Answer
(a) 1 and 4
(b) 2 and 3
(c) 3
The position of a particle moving along the x axis is given in
centimeters by x = 9.75 + 1.50t3, where t is in seconds.
(a) Calculate the average velocity during the time interval t =
2.00 s to t = 3.00 s;
(b) Calculate the instantaneous velocity at t = 2.00 s.
(c) Calculate the instantaneous velocity at t = 3.00 s.
(d) Calculate the instantaneous velocity at t = 2.50 s.
(e) Calculate the instantaneous velocity when the particle is
midway between its positions at t = 2.00 s and t = 3.00 s.
(f) Graph x versus t and indicate your answers graphically.
Answer
(a) 28.5 cm/s;
(b) 18.0 cm/s;
(c) 40.5 cm/s;
(d) 28.1 cm/s;
(e) 30.3 cm/s
The following equations give the position x(t) of a particle in
four situations (in each equation, x is in meters, t is in seconds,
and t > 0):
(1) x = 3t - 2
(2) x = -4t2 - 2
(3) x = 2/t2
(4) x = -2
The position function x(t) of a particle moving along an x axis
is x = 4.0 - 6.0t2, with x in meters and t in seconds.
(a) At what time does the particle (momentarily) stop?
(b) Where does the particle (momentarily) stop?
(c) At what negative time does the particle pass through the
origin?
(d) At what positive time does the particle pass through the
origin?
(e) Graph x versus t for the range -5 s to +5 s.
(f) To shift the curve rightward on the graph, should we
include the term +20t or the term -20t in x(t)?
(g) Does that inclusion increase or decrease the value of x at
which the particle momentarily stops?
53
A tortoise can run with a speed of 10.0 cm/s, and a hare can
run exactly 20 times as fast. In a race, they both start at the
same time, but the hare stops to rest for 2.00 min. The tortoise
wins by 20.0 cm.
(a) Draw a position time graph for both the tortoise and the
hair. Put both critters on the same axis.
(b) How long does the race take?
(c) What is the length of the race?
(d) Solve the problem using algebra.
Answer
(a) 126 s
(b) 1260 cm
54
The Table gives the position and time of an arrow during a 4.0
second flight.
(a) Draw a motion map of the arrow's flight. make sure the
motion map is drawn to scale
(b) What is the arrow’s position at t1 = 1.5 s?
(b) What is the arrow's position at t2 = 3.0 s?
(c) What is the arrow's displacement between t1 and t2?
(d) What is the time interval corresponding to this
displacement?
56
The picture shows the motion map of a car moving north.
(a) Make a table of the car’s time and position.
(b) What is the position of the car at 2 seconds?
(c) What is the position of the car at 5 seconds?
(d) What is the change in position between 0 and 3 seconds?
(e) What is the change in position between 3 and 6 seconds?
(f) What is the change in position between 6 and 9 seconds
(g) What is another name for change in position?
Answer
(a)
(b) 4 m/s north
(c) 25 m north
(d) 9 m
(e) 27 m
(f) 45 m
(g) displacement
Answer
(a)
(b)
(c)
(d)
(e)
55
Motion Map Drawing
85.30 m
154.20 m
68.9 m
1.5 sec
57
The picture shows a ball rolling along a table at 1 second time
intervals. The position is measured using a 2 meter stick.
(a) Make a time position table of the ball shown in the picture.
(b) What is the scale of the drawing?
The diagram shows a motion map of a car moving east.
(a) Make a table of the car’s time and position
(b) What is the car’s position at 3 seconds?
(c) What is the car’s position at 5 seconds?
(d) What is the car’s displacement between 3 and 5 seconds?
Answer
Allow +/- 3
time
0
1
2
3
4
5
6
Position
0
5
20
45
78
123
176
part B scale may vary a bit but its about 33 to 1
Answer
(a)
(b) 45 ft
(c) 125 ft
(d) 80 ft
58
The figure shows the motion map of a car moving south.
(a) Make a table of the car’s time and position.
(b) What is the car’s position at 10 seconds?
(c) What is the car’s position at 15 seconds?
(d) What is the car’s position at 20 seconds?
(e) What is the car’s displacement between 0 and 5 seconds?
(f) What is the car’s displacement between 10 and 15 seconds?
(g) What is the car’s displacement between 15 and 20
seconds?
Answer
(a)
(b)
(c)
(d)
(e)
(f)
250 ft
560 ft
760 ft
210 ft
200 ft
59
A stroboscopic photograph of a Dry Ice puck as it moves from
left to right. The light flashed every tenth of a second and the
scale is in centimeters.
(a) Make a time position table of the movement of the ice
puck
(b) What is the scale of the diagram?
62
The table blow shows the movement of two objects over a 70
minute interval
(a) Draw a motion map of each object’s movement. Make
sure the motion map is drawn to scale
(b) At which positions are the displacements between objects
1 and 2 equal
(c) At what positions are the path lengths between the two
objects equal?
Answer
1 cm = .16 cm
60
The picture shows the movement of a ball. The light flashes
every 1/10-second.
(a) Make a time position table of the movement of the ball.
(b) If the scale at the top represents a meter stick, what is the
scale of the picture
Answer
(a)
(b) t10 - t30
(c) t10 - t30
63
Answer
61
The table gives the position and time of an object during a 7.0second time interval.
(a) Draw a motion map of the object’s movement. Make sure
the motion map is drawn to scale
(b) What is the object’s position at t1 = 2 s?
(c) What is the object’s position at t2 = 5.0 s?
(d) What is the object’s displacement between t1 and t2?
(e) What is the time interval corresponding to this
displacement?
The diagram shows three cars traveling south. Car X is moving
at 45 mph, Car Y at 35 mph, and Car Z at 30 mph. Assume
Car X is 40 miles north of the reference line, Car Y is 20 miles
south of the reference line and Car Z is 30 miles south of the
reference line
(a) Make a position time table for each of the cars.
(b) Draw an accurate motion map of the three cars.
(c) At what time does Car X catch up with Car Y and Car Z?
(d) What was the path length of each car when all three cars
are simultaneously at the same position.
Answer
(a)
(b)
(c)
(d)
64
Answer
(a)
(b)
(c)
(d)
(e)
Use the motion map showing three runners.
(a) Make a position time table for each runner (assume the
time flashes are equal and the same for each runner)
(b) Make a position time graph for each runner. Place all three
runners on the same graph.
(c) Do Runners A, B and C ever meets at the same point?
explain your answers.
-2m
2m
4m
3 sec
Answer
(a)
(b)
(c)
65
A girl winds up a toy car and places it on the floor. When she
lets go of the car it moves as shown in the strobe picture. The
car is shown at 2 s intervals
(a) Make a time position table of the toy car shown in the
picture. Note: Each interval on the graph represents 0.5
meters
(b) Make a position time graph of the motion of the car?
68
The picture shows a ball rolling toward a wall, hits the wall
and rolls backward. On the way back it rolls over some felt
and slows down. The position marks on the drawing represent
1 meter and the times are 1/5 second.
(a) Make a position-time table of the ball’s motion.
(b) Make a position-time graph of the ball’s motion
Answer
(a)
(b)
Answer
66
The picture shows Joey and Merinda racing around a lamp post
and back to the sidewalk. While Joey is still running towards
the street lamp, Merinda will pass him on her way back to the
sidewalk.
(a) Make a position time table of Joey and Merinda
(b) Make a position time graph of Joey and merinda
(c) Make a motion map of Joey and Merinda racing by
drawing symbols to show the positions of Merinda and Joey
every second. We have drawn the first few symbols for you.
(d) How far from the street lamp will this happen?
(e) At what time will this happen?
(f) What is their position relative to their starting point when
this happens?
(a) table
(b) graph
69
The hare is traveling at 1 m/s while the turtle is traveling at 0.5
m/s.
(a) Make a table showing the position of the hair and turtile.
stop when the hare catches the turtle. Use 5 second intervals.
(b) Draw a motion map to show when the hair catches the
turtle.
(c) Draw a position time graph of the motion of the hare and
the turtle.
(d) At what time does the hare catch the turtle?
(e) At what position does the hare catch the turtle?
Answer
(a) table
(b) motion map
(c) graph
(d) 24 seconds
(e) 19 meters
Answer
(a) table
(b) graph
(c) motion map
(d)
(e)
(f)
67
A girl winds up a toy car and places it on the floor. When she
lets go of the car it moves as shown in the strobe picture. Her
brother releases a similar car in the opposite direction The cars
are shown at 2 s intervals
(a) Make a table comparing the position and times of the two
cars shown in the motion map. Note: The intervals shown on
the picture represent 1.5 meters.
(b) Make a position-time graph of the two cars. Place both
cars on the same graph.
Answer
(a) table
(b) graph
70
The picture show a motion map of an airplane landing
(a) Make a position- time table of the airplane’s motion.
(b) Make a position-time graph of the airplane’s motion.
Answer
(a)
T1 = 240
T2 = 150
T3 = 90
T4 = 45
T5 = 7.5
(b) graph
71
The picture show a motion map of a car traveling in a straight
line.
(a) Make a position- time table of the car’s motion.
(b) Make a position-time graph of the car’s motion.
75
If the average velocity of a duck is zero in a given time
interval, what can you say about the displacement of the duck
for that interval?
Answer
the duck’s displacement must also be zero
Answer
76
(a) table
(b) graph
Does knowing the displacement between the positions of two
objects give you enough information to locate the objects?
Explain.
Answer
72
The picture show a motion map of a car traveling in a straight
line.
(a) Make a position- time table of the car’s motion.
(b) Make a position-time graph of the car’s motion.
No, because a single displacement value could correspond
to a variety of different positions of the objects.
77
Answer
(a) table
(b) graph
73
The figure shows two ball traveling in the same direction. The
first ball is traveling at 2 cm/s and located at the -3 cm mark.
The second ball is traveling at 5 cm/s and located at the 4 cm
mark. Make sure you indicate the time interval you are using to
answer each of the questions below.
(a) Make a position time table for each of the two balls.
(b) Make a position-time graph for each of the balls.
(c) Complete the motion map to show when the second ball
catches up with the first ball.
(d) At what position does the second ball catch up with the first
ball?
(e) At what time does the second ball catch up with the first
ball?
Answer
Two identical sailboats with different colored sails are
traveling to the right in still water. The positions of the
sailboats at successive one-second time intervals are shown in
the diagram . Use a scale of 1 mm = 10 meters.
(a) Make a table of the sailboat positions at each interval of
time.
(b) Which sailboat has the greater displacement after 1 second
(c) Which sailboat has the greater displacement after 2
seconds
(d) Which sailboat has the greater displacement after 3
seconds?
Answer
78
The diagram shows a strobe photograph of the movement of a
car at equal intervals of time.
(a) Make a table of the car’s position at each interval of time.
(b) Make a graph of the car’s position verses time?
(b) What is the cart’s displacement during the 8 second
interval?
(c) What is the cart’s path length during the 8 second time
interval?
(a) table
(b) graph
(c) motion map
(d)
(e)
74
The picture show a motion map of a car traveling in a straight
line.
(a) Make a position- time table of the car’s motion.
(b) Make a position-time graph of the car’s motion.
Answer
(a)
(b)
Answer
(a)
(b)
(c)
79
A girl winds up a toy car and places it on the floor. When she
lets go of the car it moves as shown in the strobe picture. The
car is shown at 2 s intervals. Note: Each mark on the drawing
represents 1 meter
(a) Make a table of the car position at each time.
(b) Make a graph of the car’s position at each time.
(c) What is the cart’s displacement at 12 seconds
(d) What is the path length the car moved at 12 seconds?
84
Answer
5.436 m/s
85
Answer
(a)
(b)
(c)
(d)
80
While John is traveling along an interstate highway, he notices
a 160-mile marker as he passes through a town. Later John
passes another mile marker, 115.
(a) What is the distance (path length) between town and John's
current location?
(b) What is the displacement between town and John’s current
location?
(c) What is John's current position?
The Olympic record for the marathon is 2 h, 9 min, 21 s. The
marathon distance (path length) is 42.19 km. Determine the
average speed in m/s of a runner achieving this record.
In a 4-hour period, a hiker walked 5.0-km north during the first
hour and 4.4-km south during the second hour. After resting
for an hour, the hiker walked 4.6 south km during the fourth
hour.
(a) What was the average velocity during the first two hours;
(b) What was the average velocity during the first three hours;
(c) What was the average velocity during the entire four-hour
period?
Answer
(a) 0.3 km/hr
(b) 0.2 km/hr N
(c) -1 km/hr
86
The Sears Tower in Chicago is 443 m tall. Joe wants to set the
world's stair-climbing record and runs all the way up to the
roof of the tower in 12.0 min. On the way back down, he is so
tired that it takes him twice as long to descend. What is Joe's
average speed (in m/s) during the entire trip?
Answer
(a) 45 miles assuming that John is traveling in a straight
line if not cannot tell from the information.
(b) 45 miles
(c) +115
81
While John is traveling along a straight interstate highway, he
notices that the mile marker reads 260. John travels until he
reaches the 150-mile marker and then retraces his path to the
175-mile marker.
(a) What is John's displacement from the 260-mile marker?
(b) What is Jon's distance from the 260-mile mark?
(c) What is the total path length that John traveled?
Answer
0.410 m/s
87
Heather and Matthew take 34 min to walk eastward along a
straight road to a store 2.0 km away. What is their average
velocity in m/s?
Answer
0.98 m/s
to the east
Answer
(a) -85 mi.
(b) +85 mi
(c) 135 mi.
82
88
Here are three pairs of initial and final positions, respectively,
along an x axis. Which pairs give a negative displacement:
(a) -3 m, +5 m
(b) -3 m, -7 m
(c) +7 m, -3 m
Answer
(a)
(b)
(c)
(d)
Answer
b and c
83
Eugene is 75.0 km due south of Salem. If Joe rides from Salem
to Eugene on his bike in 6.00 h, what is his average velocity?
Answer
12.5 km/h
3.47 m/s
to the south
A bus stop is 0.68 km down he street from the museum and it
takes you 9.5 minutes to walk north from the bus stop to the
museum entrance.
(a) Draw a picture of the situation
(b) What is your average speed in m/s?
(c) What is your direction?
(d) What is your average velocity?
89
Picture
1.2 m/s
North.
1.2 m/s N
El Paso is 1142 km south of Denver. A bus makes the trip from
El Paso to Denver in 15.08 h,
(a) What is its average velocity in km/hr?
(b) What is its average velocity in m/s?
Answer
(a)
(b) 21.03 m/s S
90
You live 10.0 km from your school and the bus takes 0.53 h to
reach the school from your house driving due east.
(a) Draw a picture of the situation
(a) What is the average velocity of the bus in km/hr?
(b) What is the average velocity of the bus in m/s?
94
Answer
(a) Picture
(b) 10 km/hr E
(c) 5.3 m/s E
91
During a race on level ground, Andrea covers 825 m in 137 s
while running due west. Find Andrea’s average velocity.
A girl winds up a toy car and places it on the floor. When she
lets go of the car it moves as shown in the strobe picture. The
car is shown at 2 s intervals. Note: Each mark on the scale
stands for 30 cm.
(a) What is the average velocity of the car for the first 4
seconds
(b) What is the average velocity of the car from 4 to 8
seconds?
(c) What is the average velocity of the car from 8 to 10
seconds?
(d) What is the average velocity of the car from 10 to 12
seconds?
(e) What is the average velocity of the car from 12 to 14
seconds?
(f) What is the average velocity of the car for the entire 14
second run?
Answer
6.02 m/s
to the west
92
An athlete swims from the north end to the south end of a 50.0m pool in 20.0 s and makes the return trip to the starting
position in 22.0 s.
(a) What is the average velocity for the first half of the swim?
(b) What is the average velocity for the second half of the
swim?
(c) What is the average velocity for the roundtrip?
(d) What is the average speed for the entire swim?
Answer
(a)
(b)
(c)
(d)
(e)
(f)
95
Answer
(a) 2.50 m/s
to the south
(b) 2.27 m/s
to the north
(c) 0.0 m/s
(d) 2.38 m/s
93
The figure shows a car’s position over a six second run.
(a) What is the average velocity of the car for each one-second
interval?
(b) What is the car’s average velocity during the entire six
second run?
Two identical sailboats with different colored sails are
traveling to the right in still water. The positions of the
sailboats at successive one-second time intervals are shown in
the diagram . Use a scale of 1 mm = 10 meters.
(a) Which sailboat has the greater average velocity over the
first two seconds?
(b) Which sailboat has the greater average velocity over the
entire 4-second time interval?
Answer
(a)
(b)
96
Answer
The figure shows a strobe photograph of a ball over a 6 interval
time period. Each interval is 1/20 of a second.
(a) What is the average velocity of the ball during each time
interval?
(b) What is the average velocity of the ball for the entire time
period shown in the picture?
(a)
(b)
Answer
(a)
(b)
97
The picture show the motion map of a toy car traveling along a
stright line. Assume each mark is 10 cm.
(a) Make a position time table of the toy car shown in the
picture.
(b) Make a position time graph of the toy car for the entire
time shown.
(c) Describe the motion of the car in words.
100
The data in the table gives the position and clock readings of
an object moving east during a four second time interval. Use
the data to calculate the average velocity during each onesecond interval.
Answer
(a)
(b)
(c)
98
The table gives the position and clock readings of an arrow
traveling south during a 4.0 second flight.
(a) Draw a motion map of the arrow’s flight.
(b) Use the data in the table to calculate the average velocity
for the time interval between 1.5 and 3.0 seconds
(c) Use the data in the table to calculate the average velocity
for the time interval between 1.0 and 3.0 seconds.
Answer
2.7 m/s,
18.9 m/s
51.3 m/s
99.9 m/s
101
Positions (in meters) and times (in seconds) are shown in the
table for a moving object. Determine which one-second-time
interval corresponds to the greatest velocity.
Answer
Answer
(a) Picture
(a) 46 m/sec
(b) 48 m/sec
99
2 sec,
3 sec
102
The data in the table gives the position and clock readings for
an object moving east during a four second time interval.
(a) Determine the average velocity of the object between t1 = 2
s to t2 = 4 s.
(b) Determine the average speed of the object between t1 = 2 s
to t2 = 4 s.
A cross-country runner runs 5.0 km east along the course, then
turns around and runs 5.0 km west along the same path. She
returns to the starting point in 40 min.
(a) What his her average speed in km/hr?
(b) What is her average speed in m/s?
(c) What is her average velocity?
Answer
(a) 15 km/h
(b) 4.17 m/s
(c) 0
Answer
A high-performance jet plane, practicing radar avoidance
maneuvers, is in horizontal flight 35 m above the level ground.
Suddenly, the plane encounters terrain that slopes gently
upward at 4.30, an amount difficult to detect.
(a) Draw a picture of situation described above
(b) How much time does the pilot have to make a correction to
avoid flying into the ground? The speed of the plane is 1300
km/h.
(a) 75.6 m/sec E
(b) 75.6 m/s
Answer
103
(a)
(b)
104
A mining cart is pulled up a hill at 20 km/h and then pulled
back down the hill at 35 km/h through its original level. (The
time required for the cart's reversal at the top of its climb is
negligible.)
(a) Draw a picture of the situation
(b) What is the average speed of the cart for its round trip,
from its original level back to its original level?
(c) What was the average velocity of the entire trip
109
The figure shows four paths along which objects move from a
starting point to a final point, all in the same time interval. The
paths pass over a grid of equally spaced straight lines.
(a) Rank the paths according to the average velocity of the
objects, greatest first.
(b) Rank the paths according to the average speed of the
objects, greatest first.
Answer
(a) Picture
(b) 25 km/h
(c) 0 m/s
105
An airplane travels 2400 km at a speed of 800 km/h, and then
encounters a tailwind that boosts its speed to 1000 km/h for the
next 1800 km.
(a) What was the total time (hours) for the trip?
(b) What was the average speed in m/s of the plane for this
trip?
Answer
Answer
(a) all tie;
(b) 4, tie of 1 and 2, then 3
110
(a) 4.8 hours
(b) 50.63 m/s
875 km/hr
106
107
Two locomotives shown in the figure approach each other on
parallel tracks. Each has a speed of 120 km/h with respect to
the ground. If they are initially 8.5 km apart, how long will it
be before they pass each other?
During a hard sneeze, your eyes might shut for 0.50 s. If you
are driving a car at 90 km/h during such a sneeze, how far does
the car move during that time?
Answer
Answer
13 m
127 s
On average, an eye blink lasts about 100 ms. How far does a
MiG-25 "Foxbat" fighter travel during a pilot's blink if the
plane's average velocity is 3400 km/h?
111
When the legal speed limit for the New York Thruway was
increased from 55 mi./h (=88.5 km/h) to 65 mi./h (=105 km/h),
how much time was saved by a motorist who drove the 435 mi.
(=700 km) between the Buffalo entrance and the New York
City exit at the legal speed limit?
Answer
94.4 m
108
The 1992 world speed record for a bicycle (human powered
vehicle) was set by Chris Huber. His time through the
measured 200 m stretch was a sizzling 6.509 s, at which he
commented, "Cogito ergo zoom!" (I think, therefore I go fast!).
In 2001, Sam Whittingham beat Huber's record by 19.0 km/h.
What was Whittingham's time through the 200 m?
Answer
5.554 s
Answer
1 hour 13 minutes
1.23 hours
.134 km/min.
112
You drive on Interstate 10 from San Antonio to Houston, half
the time at 35.0 mi./hr (= 56.3 km/h) and the other half at 55.0
mi./h (= 88.5 km/h). On the way back you travel half the
distance at 35.0 mi./h and the other half at 55.0 mi./h.
(a) What is your average speed from San Antonio to Houston
(b) What is your average speed from Houston back to San
Antonio?
(c) What is your average speed for the entire trip
(d) What is your average velocity for the entire trip?
(e) Graph x versus t for (a), assuming the motion is all in the
positive x direction.
(f) Describe how the average velocity can be found on the
graph.
115
Answer
Answer
(a)
(b)
(c)
(d)
(e)
(f)
(a) 73 km/h;
(b) 68 km/h;
(c) 70 km/h;
(d) 0
45.0 mi./h (72.4 km/h)
42.8 mi./h (68.8 km/hr)
43.9 mi./h (70.6 km/h)
0
116
113
You drive on Interstate 10 from San Antonio to Houston, half
the time at 55 km/h and the other half at 90 km/h. On the way
back you travel half the distance at 55 km/h and the other half
at 90 km/h.
(a) What is your average speed from San Antonio to Houston?
(b) What is your average speed from Houston back to San
Antonio?
(c) What is your average speed for the entire trip?
(d) What is your average velocity for the entire trip?
(e) Sketch x versus t for (a), assuming the motion is all in the
positive x direction. Indicate how the average velocity can be
found on the sketch.
128 km/h
Answer
(a) 73km/h;
(b) 68km/h;
(c) 70km/h;
(d) 0
You are to drive to an interview in another town, at a distance
of 300 km on an expressway. The interview is at 11:15 A.M.
You plan to drive at 100 km/h, so you leave at 8:00 A.M. to
allow some extra time. You drive at that speed for the first 100
km, but then construction work forces you to slow to 40 km/h
for 40 km. What would be the least speed needed for the rest of
the trip to arrive in time for the interview?
You are to drive to an interview in another town, at a distance
of 300 km on an expressway. The interview is at 11:15 A.M.
You plan to drive at 100 km/h, so you leave at 8:00 A.M. to
allow some extra time. You drive at that speed for the first 100
km, but then construction work forces you to slow to 40 km/h
for 40 km. What would be the least speed needed for the rest of
the trip to arrive in time for the interview?
Answer
117
114
You drive on Interstate 10 from San Antonio to Houston, half
the time at 55 km/h and the other half at 90 km/h. On the way
back you travel half the distance at 55 km/h and the other half
at 90 km/h.
(a) What is your average speed from San Antonio to Houston?
(b) What is your average speed from Houston back to San
Antonio?
(c) What is your average speed for the entire trip?
(d) What is your average velocity for the entire trip?
(e) Sketch x versus t for (a), assuming the motion is all in the
positive x direction. Indicate how the average velocity can be
found on the sketch.
Simpson drives his car with an average velocity of 24 m/s
toward the east. How long will it take him to drive 560 km on a
perfectly straight highway?
Answer
6.5 h
118
The peregrine falcon is the fastest of flying birds (and, as a
matter of fact, is the fastest living creature). A falcon can
descend with a speed of 2.50 x 102 km/h. If a falcon flies at this
speed for 2.00 s and then flies another 1.00 x 102 m in 2.50 s,
what is the falcon's average speed for the entire flight?
Answer
191 km/h
53.1 m/s
Answer
128 km/h
119
A bus traveled south along a straight path for 3.2 h with an
average velocity of 88 km/h, stopped for 20.0 min, then
traveled south for 2.8 h with an average velocity of 75 km/h.
(a) What is the average velocity for the total trip?
(b) What is the displacement for the total trip?
Answer
(a) 78 km/h to the south
(b) 490 km to the south
120
The black mamba is one of the world's most poisonous snakes,
and with a maximum speed of 18.0 km/h, it is also the fastest.
Suppose a mamba waiting in a hideout sees prey and begins
slithering toward it at its maximum speed. After 2.50 s, the
mamba realizes that its prey can move faster than it can. The
snake then turns around and slowly returns to its hide-out in
12.0 s.
(a) What is the mamba's average speed?
(b) What is the mamba's average velocity?
124
The figure is a graph of a particle's position along an x axis
versus time.
(a) At time t = 0, what is the sign of the particle's position?
(b) Is the particle's velocity positive, negative, or 0 at t = 1 s?
(c) Is the particle's velocity positive, negative, or 0 at t = 2 s?
(d) Is the particle's velocity positive, negative, or 0 at t = 3 s?
(e) How many times does the particle go through the point x =
0?
Answer
(a) 1.72 m/s
(b) 0 m/s
121
Sally travels by car from one city to another. She drives for
30.0 min at 80.0 km/h, 12.0 min at 105 km/h, and 45.0 min at
40.0 km/h, and she spends 15.0 min eating lunch and buying
gas.
(a) Determine the average speed for the trip.
(b) Determine the average velocity for the trip.
(c) Determine the total distance traveled
Answer
(a) negative;
(b) positive;
(c) zero;
(d) negative;
(e) twice
Answer
(a) 535 km/h
(b) 535 km/h
(c) 91.0 km
125
122
What is the shortest possible time in which a bacterium could
move at a speed of 3.5 mm/s across a petri dish with a diameter
of 8.4 cm?
The graph of x versus t in the figure is for a particle in straightline motion. State, for each of the intervals AB, BC, CD, and
DE, whether the velocity v is positive, negative, or 0 a
Answer
24 s
123
A child can push a shopping cart at a speed of 1.5 m/s. How
long would it take this child to push the cart down an aisle with
a length of 9.3 m?
Answer
Answer
AB = positive
BC = Positive
CD = Zero
DE = Negative
6.2 s
126
In 1 km races, runner 1 on track 1 (with time 2 min, 27.95 s)
appears to be faster than runner 2 on track 2 (2 min, 28.15 s).
However, length L2 of track 2 might be slightly greater than
length L1 of track 1. How large can L2 - L1 be for us still to
conclude that runner 1 is faster?
Answer
1.4 m
127
Two boys start running straight toward each other from two
points that are 100 m apart. One runs with a speed of 5 m/s,
while the other moves at 7 m/s. How close are they to the
slower one's starting point when they reach each other?
Answer
41 meters
128
The picture shows the motion map of a car moving north.
(a) Plot the position-time graph of the motion.
(b) What does the graph reveal about the motion of the car?
(c) Determine the distance traveled by the car at the end of 9 s
131
Use the figure to answer the following questions?
(a) What is the total distance (path length) traveled during the
recorded time interval?
(b) What is the displacement?
Answer
129
Answer
The picture shows the motion map of a car moving north.
(a) Plot the position-time graph of the motion.
(b) What does the graph reveal about the motion of the car?
(c) Determine the distance traveled by the car at the end of 30
s
(a) 5.0 m
(b) +5.0 m
132
The picture shows the motion map of a car moving north.
(a) Plot the position-time graph of the motion.
(b) What does the graph reveal about the motion of the car?
(c) Determine the distance (path length) traveled by the car at
the end of 9 s
Answer
130
The position of an object during a 20-second time interval is
shown in the figure
(a) What is the object’s path length between t = 0 s and t = 5 s.
(b) What is the object’s path length between t = 5 s and t = 10
s.
(c) What is the object’s path length between t = 10 s and t =
15 s.
(d) What is the object’s path length between t = 15 s and t =
20 s.
(e) What is the object’s path length between t = 0 s and t = 20
s
Answer
(a)
(b)
(c)
133
The picture shows the movement of a ball hitting a wall and
rebounding backward. The light flashes every 1/2-second. the
intervals stand for 0.5 m
(a) Plot the position-time graph of the motion.
(b) What does the graph reveal about the motion of the ball?
(c) Determine the distance (path length) traveled by the car at
the end of 20 s.
(d) Determine the displacement traveled by the car at the end
of 20 seconds.
Answer
Answer
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
10 m
30 m
0m
40 m
80 m distance
134
The picture shows the movement of a ball. The light flashes
every 2-seconds
(a) Plot the position-time graph of the motion.
(b) What does the graph reveal about the motion of the ball?
(c) Determine the distance (path length) traveled by the car at
the end of 12 s.
137
The position traveled by an arrow is given in the table .
(a) Draw a position time graph
(b) Use interpolation and the data in the table to estimate the
position of the arrow at t = 0.75 s.
Answer
(a)
(b)
(c)
135
The diagram shows a strobe photograph (motion map) of the
movement of a car at equal intervals of time.
(a) Make a position-time table of the motion of the car.
(b) Plot the position-time graph of the motion.
(c) What does the graph reveal about the motion of the cart?
(d) Determine the distance (path length) traveled by the car at
the end of 8th time interval.
Answer
(a) graph
(b) 45 m
138
An object’s position in meters and times (in seconds) are
recorded in the table.
(a) Draw the graph
(b) Use (linear) interpolation to obtain the object’s position at
t = 0.5 s and
(c) Use (linear) interpolation to obtain the object’s position at t
= 2.75 s.
Answer
(a) table
(b) graph
(c)
(d)
136
The position traveled by a car over a 10-s time interval
increased as shown in the table .
(a) Plot the position-time graph of the motion.
(b) What does the graph reveal about the motion of the car?
(c) Determine the distance traveled by the car at the end of 5.5
s
Answer
(a) graph
(b) linear constant velocity
(c) about 97
Answer
(a) graph
(b) 0.25 m
(c) exact 7.56
7 or 8 from graph
139
The position of an object during a 20-second time interval is
shown in the figure.
(a) What is the object’s displacement between t = 0 s and t =
5 s.
(b) What is the object’s displacement between t = 5 s and t =
10 s.
(c) What is the object’s displacement between t = 10 s and t =
15 s.
(d) What is the object’s displacement between t = 15 s and t =
20 s.
(e) What is the object’s displacement between t = 0 s and t =
20 s
141
The position a steel ball rolls down an incline at the end of
each second of travel is given in the table .
(a) Draw a position-time graph of the motion of the ball.
(b) What type of curve is the line of the graph?
(c) What distance (path length) has the ball rolled at the end of
2.2 s?
Answer
(a)
(b) parabola
(c) 10 m
Answer
(a)
(b)
(c)
(d)
(e)
140
10 m
30 m
0m
-40 m
0 displacement
142
The figure is a graph of the position of an object over a given
time interval.
(a) Use the position-time graph to find how far the object
travels between t = 0 s and t = 40 s
(b) Use the position-time graph to find how far the object
travels between t = 40 s and t = 70 s
(c) Use the position-time graph to find how far the object
travels between t = 90 s and t = 100 s
The following table gives the total vertical distance a ball is off
the ground during each second of flight.
(a) Draw a position-time graph of the motion of the ball.
(b) How far off the ground is the ball at the end of 0.5 s?
(c) When would the ball again be this distance from the
ground?
Answer
(a) 400 m
(b) 0
(c) - 200 m
Answer
(a) Upside down parabola
(b) 13.5 m,
(c) 5.5 s
143
The graph of x versus t in the figure is for a particle in straightline motion. State, for each of the intervals AB, BC, CD, and
DE, whether the velocity v is positive, negative, or 0
Answer
AB = Positive
BC = Zero
CD = Positive
DE = Positive
144
A position-time graph of an object is shown in the figure .
(a) Use the position-time graph to find the object's velocity
between t = 0 s and t = 5 s.
(b) Use the position-time graph to find the object's velocity
between t = 5 s and t = 10 s.
(c) Use the position-time graph to find the object's velocity
between t = 10 s and t = 15 s.
(d) Use the position-time graph to find the object's velocity
between t = 15 s and t = 20 s.
(e) Use the position-time graph to find the object's velocity
between t =0 s and t = 20 s
146
The figure is the position-time graph for a squirrel running
along a clothesline.
(a) What is the squirrel's displacement during the time interval
from t = 0.0 s to t = 3.0 s?
(b) What is the squirrel's average velocity during this interval?
Answer
(a) -2.0 m
(b) -.67 m/s
147
Answer
(a)
(b)
(c)
(d)
(e)
145
The position traveled by a car over a 10-s time interval
increased as shown in the table.
(a) Draw a position time graph of the motion of the car.
(b) Determine the speed of the car in meters/second
(c) Determine the speed of the car in km/hr.
2 m/s
6 m/s
0 m/s
-8 m/s
0 m/s
The position of an object over time is shown in the figure .
(a) Find the average velocity of an object between t = 10 and
12 s
(b) Find the average velocity of an object between t = 14 and
18 s
(c) Find the average velocity of an object between t = 20 and
24 s
(d) Find the average velocity of an object between t = 26 and
30 s
Answer
(a) graph
(b) 17.5 m/s
(c) 63 km/hr
148
The position a piece of ice slid down a 7.5-m slope at the end
of each second after its release is given in the table .
(a) Make a position-time graph of its motion.
(b) How far will the ice have traveled at the end of 3.5 s?
(c) Determine the speed of the ice at that time from the graph.
Answer
(a)
(b)
(c)
(d)
+ 2.5 m/s
-1.25 m/s
-3.25 m/s
+.4 ms/
Answer
(a) graph
(b) 3.6 m
(c) 1.9 m/sec
149
A position-time graph of an object is shown in the figure .
(a) Use the position-time graph to find the object's velocity
between t = 0 s and t = 5 s.
(b) Use the position-time graph to find the object's velocity
between t = 5 s and t = 10 s.
(c) Use the position-time graph to find the object's velocity
between t = 10 s and t = 15 s.
(d) Use the position-time graph to find the object's velocity
between t = 15 s and t = 20 s.
(e) Use the position-time graph to find the object's velocity
between t =0 s and t = 20 s
152
A position time graph for an object is shown in the figure .
(a) Determine the slope of the object at 1 s
(b) Determine the slope of the object at 4 s.
Answer
(a) 6.4 m/s
(b) 2.4 m/s
153
Answer
(a)
(b)
(c)
(d)
(e)
150
2 m/s
6 m/s
0 m/s
-8 m/s
0 m/s
A position time graph for an object is shown in the figure .
(a) Obtain the velocity of the object at 1 s
(b) Obtain the velocity of the object at 2 s
(c) Obtain the velocity of the object at 4 s
Two cars are headed in the same direction; one traveling 60
km/h is 20 km ahead of the other traveling 80 km/h.
(a) Draw a position-time graph showing the motion of the
cars.
(b) Use your graph to find the time when the faster car
overtakes the slower one.
Answer
Answer
(a)
(b) 1 h
151
From the position-time graph shown in the figure construct a
table showing the average velocity of the object during each
10-s interval over the entire 100 s.
(a) -.666 m/s
(b) -4 m/s
(c) -1.25 m/s
154
An object moves as shown in the graph shown in the figure .
Calculate the object's velocity at t = 3 s.
Answer
Answer
0-10 10 m/s
10-20 10 m/s
20-30 10 m/s
30-40 10 m/s
40-50 0 m/s
50-60 0 m/s
60-70 0 m/s
70-80 -10 m/s
80-90 -10 m/s
90-100 -20 m/s
-10 m/s
155
On the position-time graph shown in the figure, what
represents the velocity?
158
The figures shows position-time graphs of the straight-line
movement of two brown bears in wildlife preserve.
(a) Which bear has the greater average velocity over the entire
period?
(b) Which bear has the greater velocity at t= 10.0 min?
(c) Is the velocity of bear A always positive? Explain
(d) Is the velocity of bear B ever negative? Explain.
Answer
The slope of the line at each point.
156
The position-time graph for a bug crawling along a line is
shown in the figure . Determine whether the velocity is
positive, negative, or zero at each of the times marked on the
graph.
Answer
(a)
(b)
(c)
(d)
159
Bear B
Bear A
No
No
A position time graph for an object is shown in the figure.
(a) Determine the slope of the object at 2 s
(b) Determine the slope of the object at 3 s.
Answer
t1; negative
t2; positive
t3; positive
t4; negative
t5; zero
157
Use the position-time graph in the figure to answer the
following questions:
(a) During which time interval(s) is the magnitude of the
velocity (speed) decreasing?
(b) During which time interval(s) is the magnitude of the
velocity (speed) increasing
Answer
(a)
(b)
160
A position time graph for an object is shown in the figure .
(a) What is the average velocity between 3 s and 5 s?
(b) What is the average velocity between 0 s and 4 s?
Answer
(a) 0 to t1
t1 to t2
t3 to t4
t4 to t5
(b) t1 to t2
t2 to t3
t3 to t4
Answer
(a) 7.5 m/s
(b) 7.5 m/s
161
162
A position time graph for an object is shown in the figure .
(a) Obtain the average velocity of the object between 1s and 4s
(b) Obtain the average velocity of the object between 0.2 s and
3s
(c) Obtain the average velocity of the object between 1.5 s and
3.4 s
164
Car A moves at a constant speed while car B has a changing
velocity.
(a) Find the instantaneous speed of car B at 2.0 s.
(b) Find the instantaneous speed of car A at 2.0 s.
(c) Find the instantaneous speed of car B at 9.0 s.
(d) Find the instantaneous speed of car B at 9.0 s.
Answer
Answer
(a)
(b)
(c)
(a)
(b)
(c)
(d)
For the position time graph shown in the figure, determine the
velocity at t = 2 sec.
165
Simpson drives his car with an average velocity of 24 m/s
toward the east. He drives 560 km on a perfectly straight
highway
(a) How much time would Simpson save by increasing his
average velocity to 26 m/s east?
(b) Sketch a position time graph of his two speeds.
Answer
(a) 0.5 h
(b) graph
166
Answer
163
A ball is thrown straight up into the air.
(a) Draw a position-time graph of the ball
(b) Calculate the ball’s instantaneous velocity at t = 2 s.
(c) Calculate the ball’s instantaneous velocity at t = 3 s.
(d) Calculate the ball’s instantaneous velocity at t = 4 s.
Time
(s)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Answer
(a) app 10 m/s
(b) 0 m/s
(c) app -10 m/s
Distance
(m)
0.0
24.5
39.2
44.1
39.2
24.5
0.0
To qualify for the finals in a racing event, a race car must
achieve an average speed of 250 km/h on a track with a total
length of 1600 m.
(a) If a particular car covers the first half of the track at an
average speed of 230 km/h, what minimum average speed must
it have in the second half of the event to qualify?
(b) Show how you would solve this problem using a graph.
Answer
(a) 280 km/hr
(b) explain
167
Emily takes a trip, driving with a constant velocity of 89.5
km/h to the north except for a 22.0-min rest stop. If Emily's
average velocity is 77.8 km/h to the north, how long does the
trip take?
Answer
2.81 h
168
A tortoise can run with a speed of 10.0 cm/s, and a hare can
run exactly 20 times as fast. In a race, they both start at the
same time, but the hare stops to rest for 2.00 min. The tortoise
wins by 20.0 cm.
(a) Draw a position time graph for both the tortoise and the
hair. Put both critters on the same axis.
(b) How long does the race take?
(c) What is the length of the race?
(d) Solve the problem using algebra.
Answer
(a)
(b) 126 s
(c) 1260 cm
(d)
169
Runner A is initially 6.0 km west of a flagpole and is running
with a constant velocity of 9.0 km/h due east. Runner B is
initially 5.0 km east of the flagpole and is running with a
constant velocity of 8.0 km/h due west.
(a) Make a position time table for the two runners
(b) Draw a position time graph for the runners
(c) How far are the runners from the flagpole when their paths
cross?
(d) Solve the problem by algebra.
Answer
(a) table
(b) graph
(c) 0.2 km
west of the flagpole
(d) algebra solution
170
Ann is driving down a street at 55 km/h. Suddenly a child runs
into the street. It takes Ann 0.75 s to react and apply the brakes.
(a) Draw a position time graph of the motion
(b) How many meters will she have moved before she begins
to slow down?
Answer
(a) graph
(b) 11.5 m
171
To qualify for the finals in a racing event, a race car must
achieve an average speed of 250 km/h on a track with a total
length of 1600 m.
(a) If a particular car covers the first half of the track at an
average speed of 230 km/h, what minimum average speed must
it have in the second half of the event to qualify?
(b) Show how you would solve this problem using a graph.
Answer
(a) 280 km/hr
(b) explain
172
Emily takes a trip, driving with a constant velocity of 89.5
km/h to the north except for a 22.0-min rest stop. If Emily's
average velocity is 77.8 km/h to the north, how long does the
trip take?
Answer
2.81 h