Motion
Motion
Change in position with respect to change
in time
Position
The separation from the origin
Position & Time
Position-Time Graph
Position-Time Graph (2)
Average Velocity
Average velocity is the change in position
(displacement) divided by the time interval
during which the displacement took place.
If you know two of the three quantities in
this relationship, you can determine the
third mathematically.
Average Velocity
1. A car travels at 55 km/h for 6.0 hours.
How far does it travel?
2. A missile travels 2500 km in 2.2 hours.
What is its velocity?
3. How many minutes will it take a runner
to finish an 11-km race at 18 km/h?
Average Velocity
5. A businesswoman on a trip flies a total
of 23,000 km. The first day she traveled
4000 km, the second day 11,000 km, and
on the final day she was on a plane that
could travel at 570 km/h. How long was
she on the plane the final day?
Instantaneous Velocity
The velocity at a single point in time.
Instantaneous Velocity
1. Many cars require an oil change every
4000–5000 km. If this car travels without a
break for 4800 km at 120 km/h, how long
will it take to simulate one full cycle of time
without an oil change?
2. Some cars have a warranty that lasts
for up to 150,000 km. How long would it
take for the warranty to run out if the car
ran constantly at 110 km/h?
Instantaneous Velocity
3. A car is tested for 1800 km on one day, 2100
km another day, and then is driven 65 km/h for
72 hours. What is the total distance the car has
traveled?
4. The odometer on a car reads 4100 km after 3
days of tests. If the car had been tested on one
day for 1500 km, a second day for 1200 km,
then how long was the car tested the last day if it
traveled at 120 km/h while being tested?
Instantaneous Velocity
5. Car A traveled 1200 km in 8.0 h. Car B
traveled 1100 km in 6.5 h. Car C traveled 1300
km in 8.3 h. Which car had the highest average
velocity. How long would it have taken the
slowest car to travel the same distance as the
fastest car?
6. One car tested can travel 780 km on a tank of
gasoline. How long should the car be able to
travel at 65 km/h before it runs out of gas? If the
car has a 53-L tank, then what is the average
mileage of the vehicle?
Instantaneous Velocity
7. Cars Q and Z are put through an
endurance test to see if they can travel at
120 km/h for 5.0 hours. Each car has a
45-L fuel tank. Car Z must stop to refuel
after traveling for 4.2 hours. Car Q,
however, travels for 5.4 hours before
running out of gas. For each car, calculate
the average kilometers traveled for each
liter of gas (km/L).
Instantaneous Velocity
8. Refer to the problem above. How many
liters does Car Q have left in its fuel tank
after traveling for five hours at 120 km/h?
If you were to test-drive Car Q across a
desert where there were no fuel stations
available for 1200 km, how many 10-L gas
cans should you have in the car to refuel
along the way?
Motion Diagram
Vector
A quantity that has
both magnitude and
direction
3m South (-3y)
Scalar
A quantity that has
only magnitude
3m
Velocity vs. Speed
Velocity:
Total displacement
(change in position) with
respect to total time
Speed
Total distance traveled
with respect to total time
Motion Diagram
Vector Addition
Vector Addition
Vector Subtraction
Vector Addition
Tail to Tip
Vector Addition
y
3
Total distance
= 7m
Time elapsed
= 7s
X
= 4m
Y
= 3m
Total displacement = sqrt(4^2 + 3^2)=5m
(a^2+b^2=c^2)
2
Velocity = 5m/7s = 0.7m/s
1
Speed
1
2
3
4
(one second per block)
x
= 7m/7s = 1m/s
Practice Problem
Joe goes for a run. From his house, he jogs
north for exactly 5.00h at an average speed of
10.0 km/h. He continues north at a speed of 10.0
km/h for the next 30.0h. He then turns around
and jogs south at a speed of 15.0 km/h for
15.0h. Then he jogs south for another 20.0h at
5.00 km/h. He walks the rest of the way home.
How many kilometers does Joe jog in total?
How far will Joe have to walk to get home after
he finishes jogging?
Practice
1. An airplane travels at a constant speed, relative to the
ground, of 900.0 km/h.
– a. How far has the airplane traveled after 2.0 h in the air?
– b. How long does it take for the airplane to travel between City A
and City B if the cities are 3240 km apart?
– c. If a second plane leaves 1 h after the first, and travels at 1200
km/h, which flight will arrive at City B first?
2. You and your friend start jogging around a 2.00x10^3m running track at the same time. Your average running
speed is 3.15 m/s, while your friend runs at 3.36 m/s.
How long does your friend wait for you at the finish line?
Practice
3. The graph shows the
distance versus time for two
cars traveling on a straight
highway.
– a. What can you determine
about the relative direction of
travel of the cars?
– b. At what time do they pass
one another?
– c. Which car is traveling faster?
Explain.
– d. What is the speed of the
slower car?
Practice
4. You drop a ball from a height of 2.0 m. It falls
to the floor, bounces straight upward 1.3 m, falls
to the floor again, and bounces 0.7 m.
– a. Use vector arrows to show the motion of the ball.
– b. At the top of the second bounce, what is the total
distance that the ball has traveled?
– c. At the top of the second bounce, what is the ball’s
displacement from its starting point?
– d. At the top of the second bounce, what is the ball’s
displacement from the floor?
Practice
5. You are making a map of some of your
favorite locations in town. The streets run north–
south and east–west and the blocks are exactly
200 m long. As you map the locations, you walk
three blocks north, four blocks east, one block
north, one block west, and four blocks south.
– a. Draw a diagram to show your route.
– b. What is the total distance that you traveled while
making the map?
– c. Use your diagram to determine your final
displacement from your starting point.
– d. What vector will you follow to return to your starting
point?
Practice
6. An antelope can run 90.0 km/h. A
cheetah can run 117 km/h for short
distances. The cheetah, however, can
maintain this speed only for 30.0 s before
giving up the chase.
– a. Can an antelope with a 150.0-m lead
outrun a cheetah?
– b. What is the closest that the antelope can
allow a cheetah to approach and remain likely
to escape?
Practice
7. The position-time graph to the right
represents the motion of three people in an
airport moving toward the same departure gate.
– a. Which person travels the farthest during the period
shown?
– b. Which person travels fastest by riding a motorized
cart? How can you tell?
– c. Which person starts closest to the departure gate?
– d. Which person appears to be going to the wrong
gate?
Practice
8. A radio signal takes 1.28 s to travel from
a transmitter on the Moon to the surface of
Earth. The radio waves travel at 3.00x10^8
m/s. What is the distance, in kilometers,
from the Moon to Earth?
Practice
9. You start to walk toward your house eastward
at a constant speed of 5.0 km/h. At the same
time, your sister leaves your house, driving
westward at a constant speed of 30.0 km/h. The
total distance from your starting point to the
house is 3.5 km.
– a. Draw a position-time graph that shows both your
motion and your sister’s motion.
– b. From the graph, determine how long you travel
before you meet your sister.
– c. How far do you travel in that time?
Practice
10. A bus travels on a northbound street for 20.0
s at a constant velocity of 10.0 m/s. After
stopping for 20.0 s, it travels at a constant
velocity of 15.0 m/s for 30.0 s to the next stop,
where it remains for 15.0 s. For the next 15.0 s,
the bus continues north at 15.0 m/s.
– a. Construct a d-t graph of the motion of the bus.
– b. What is the total distance traveled?
– c. What is the average velocity of the bus for this
period?
Position vs. Time
Review 2.1
1. What is a motion diagram?
– A series of images showing the position of a moving object
at equal time intervals.
2. How is a particle diagram different from a motion
diagram? Which diagram is simpler?
– The particle model is a motion diagram in which the object
has been replaced by a series of single points. The particle
model is simpler than the motion diagram.
3. What are the two components used to define motion?
– Place and time
4. Give three examples of straight-line motion.
– Car, meteor, light
Review 2.2
1. What is the primary difference between a scalar and a vector?
– A vector has both magnitude and direction, while a scalar only has
magnitude.
2. What is a resultant?
– A resultant is the sum of two or more vectors.
3. A student walks 4 blocks north then stops for a rest. She then walks 9
more blocks north and rests, then finally another 6 blocks north. What is her
displacement in blocks?
– Δd = df- di
If the student’s starting point is defined as zero, the equation
becomes
Δd = df.
Thus, the student’s displacement is equal to his or her final position and the
final position is equal to the sum of all of the displacements. So,
Δd = d1+d2+d3
Δd = (4 blocks N)+(9 blocks N)+(6 blocks N) = 19 blocks N
Review 2.2
4. A runner runs 6 km east, 6 km north, 6
km west, and finally 6 km south. What is
his total displacement? Draw a diagram.
6 km West
6 km South
6 km North
Starting
Point
6 km East
Review 2.3
1. On a position-time graph, which of the two variables is
on the x-axis? Which is on the y-axis?
– Time is represented on the x-axis and position is
represented on the y-axis.
2. If the plotted line on a position-time graph is horizontal
what does this indicate?
– The object the graph represents is not moving.
3. Can the plotted line on a position-time graph ever be
vertical? Explain your answer.
– This is unlikely, as this would represent an object moving at
an infinite speed.
Review 2.3
4. A position-time graph plots the course of two
runners in a race. Their lines cross on the graph.
What does this tell you about the runners?
– They are in the same place at the same time.
5. Does the intersecting line on a position-time
graph mean that the two objects are in collision?
Explain
– The objects are in the same place at the same
time, but they are not necessarily in collision. All
that is known is that their position with reference
to the origin is the same.
Review 2.4
1. What is the difference between speed and velocity?
– Speed does not contain a direction component and velocity does. In other
words, speed is a scalar quantity and velocity is avector quantity.
2. What is the difference between average velocity and instantaneous
velocity? Give an example of each.
– Average velocity is the total distance traveled divided by the total time of
travel. An example of average velocity is a 120-mile car trip that takes 2
hours, average velocity was 60 mph.
– Instantaneous velocity is the velocity at one given instant. An example of
instantaneous velocity is the velocity recorded by a police radar gun.
3. Define all three variables in the equation v=Δd/Δt and indicate the
appropriate label for each in SI terms.
– v is velocity in m/s,
– t is time in s,
– d is distance in m.
Review 2.4
4. What is the average velocity of a car
that travels 450 km in 9.0 hours?
– v=Δd/Δt
– 450km/9.0h = 5.0x10^1
5. How far has a cyclist traveled if she has
been moving at 30 m/s for 5.0 minutes?
– v=Δd/Δt
– Δd=vΔt
– (30m/s)(3.0x10^2 s) = 9000m
Velocity vs. Time (Ch 3)