One-D Motion Practice Problems
Remember That You Should Be (1) Working These Problems In Your Homework Notebooks and (2)
Showing ALL Work. Also, The Answers Are Provided In Bold At The End of Each Problem.
Equations:
x = xf - xi
savg  s 
distance
Δt
vavg  v 
Δx
Δt
aavg  a 
Δv
Δt
1. A car travels west at 35 mph for a time period of 2.5 hours, and then travels west at 55 mph for an additional
time of 3.5 hours. What is the car’s displacement from its starting position? (280 mi, West)
2. A cheetah is known to be the fastest mammal on Earth, at least for short runs. Cheetahs have been observed
running a distance of 5.50 x 102 m with an average speed of 1.00 x 102 km/hr.
(a) How long would it take a cheetah to cover this distance at this speed? (19.8 s)
(b) Suppose the average speed of the cheetah is just 85.0 km/hr. What distance would the cheetah cover
during the same time interval calculated in (a)? (467 m)
3. An ostrich can run at speeds of up to 72 km/hr. Suppose an ostrich runs 1.5 km at a speed of 58 km/hr and
then runs another 1.5 km at a speed of 29 km/hr. What is the ostrich’s average speed during its 3.0 km run
(Hint: The answer is NOT 43.5 km/hr)? (38.5 km/hr)
4. The black mamba is one of the world’s most poisonous snakes, and with a maximum speed of 18.0 km/hr, it is
also the fastest. Suppose a mamba waiting in a hideout sees you and begins slithering toward you at
maximum speed. After 2.50 seconds, the mamba realizes it doesn’t want to bite you. The snake turns around
and slowly returns to the hideout in 12.0 seconds. Calculate
(a) The mamba’s average speed. (1.72 m/s)
(b) The mamba’s average velocity. (0 m/s)
5. In 1991 at Smith College, in Massachusetts, Ferdie Adoboe ran backward for a distance of 100 meters in 13.6
seconds. (a) What is her average speed for the run? (7.35 m/s) (b) Suppose it takes Adoboe 2.0 seconds to
achieve a speed equal to her average speed during the run. Find the her average acceleration during the first
2.0 sec. (3.68 m/s2)
Show ALL WORK for any quantitative answers.
Use the following graph to answer questions (a) through (f) below:
(a) During which portion(s) (A, B, C, D, and/or E) of
the motion is the object speeding up?
Position vs. Time
(b) During which time interval(s) is the object
slowing down?
(c) During which time interval(s) is the object
traveling at a positive constant velocity?
(d) During which time interval(s) is the object
traveling at a negative constant velocity?
(e) What is the average velocity of the object within
the 2 to 3 second time interval? (40 m/s)
(f) What is the average velocity of the object for the
whole motion, from 0 to 5 seconds? (-4 m/s)
D
C
70.0
60.0
Position (meters)
6.
50.0
B
40.0
E
30.0
20.0
A
10.0
0.0
-10.0
1
2
3
4
-20.0
-30.0
Time (seconds)
5
7.
A particle moves according to the equation
x(t) = b t2
Where x(t) is the position of the particle at time t, and b is a constant and equal to 10 m/s 2
(a) What is the average velocity for the time interval from t1 = 2 seconds, and t2 = 3 seconds? (50 m/s)
(b) What is the average velocity for the time interval from t1 = 2 seconds, and t3 = 2.1 seconds? (41 m/s)
8. Use the following graph to answer the following
questions:
Position vs. Time
(a) What is the displacement that occurs during
i. the first 10 seconds?
ii. the 10-15 second time interval?
iii. the 15-25 second time interval?
Position (meters)
100
(b) What is the average velocity during
i. the first 10 seconds? (5 m/s)
ii. the 10-15 second time interval? (0 m/s)
iii. the 15-25 second time interval? (5 m/s)
80
60
40
20
0
0
5
10
(c) Construct a line tangent to the curve at t = 5
seconds. How fast is the object moving at t=5
seconds?
15
20
Tim e (seconds)
(d) During which time interval is the object moving the fastest (0-10, 10-15, 15-25 seconds)?
9. A man jogs at a speed of 1.3 m/s. His dog waits 4.3 seconds and then takes off running at a speed of 2.4 m/s
to catch the man. How far will they have each traveled when the dog catches up with the man? (12.2 m)
10. Use the Velocity vs. Time graph to the right to answer the following questions:
(a) During which time interval(s), if any, is the speed
increasing?
Velocity vs. Time
(b) During which time interval(s), if any, is there constant,
non-zero acceleration?
(e)
During which time interval(s) is the object traveling at
constant velocity?
(f)
What is the average acceleration from 2 to 4
seconds? (-20 m/s2)
((m/s)
(d) During which time interval(s), if any, is the object
moving in the negative direction?
B
30
Velocity
(c) What is the displacement that occurs within the first 2
seconds? (40 m)
40
A
C
20
10
0
D
-10
0
1
2
3
Time (seconds)
4
5
25
11. Use the Velocity vs. Time graph from above to complete the displacement (x) and position data in the table below,
assuming that at time t = 0, the object is at position 0.
Time (s)
0
1
2
3
4
5
Position (m)
0
x (m)
12. Use the Velocity vs. Time graph and data you prepared to construct a corresponding Position vs. Time graph.
13. Use the Velocity vs. Time graph and data you prepared to construct a corresponding Acceleration vs. Time graph.
14. The velocity v(t) of a moving particle is plotted as a function of
time on the graph below. Initially, at t = 0, the particle is at a
position x = 60 m.
(b) What is the acceleration of the particle at t = 20 seconds?
At t = 30 seconds? (0.42 m/s2)
Velocity
(meters/second)
(a) What is the position of the particle at time t = 36 seconds?
(510 m)
Velocity vs. Time
20
15
10
5
0
9
18
27
36
Time (seconds)
15. A pronghorn antelope named Casey was observed to run a distance of 1.60 km with an average speed of 67.0
km/hr. If the antelope’s speed is 88.0 km/hr for the first half of this distance, what is her average speed during
the second half?
16. The fastest speed ever achieved by a vessel on water is 154 m/s. If the average acceleration of the vessel is
1.8 m/s2, how long will it take it to reach its maximum speed if it starts at rest?
17. Using the velocity vs. time graph at the right, answer the following:
(a) During which time interval(s), if any, is there constant, non-zero acceleration?
(b) What is the displacement that occurs within the first
2 seconds?
Velocity vs. Time
(c) During which time interval(s), if any, is the object
moving in the negative direction?
(e) During which time interval(s) is the object slowing
down?
(f) At what time(s) does the object change direction?
(g) What is the average acceleration from 0 to 4
seconds?
30
Velocity (m/s)
(d) During which time interval(s) is the object speeding
up?
40
A
20
D
10
0
-10 0
1
2
3
-20
-30
4
5
6
C
7
8
9
B
-40
(h) What is the average acceleration for the entire 10second time interval?
Tim e (seconds)
18. Use the Velocity vs. Time graph from above to complete the displacement (x) and position data in the table
below, assuming that at time t = 0, the object is at position 0.
Time (s)
0
1
2
3
4
5
6
7
8
9
10
x (m)
Position (m)
0
19. Use the Velocity vs. Time graph and data you prepared to construct a corresponding Position vs. Time graph.
20. Use the Velocity vs. Time graph and data you prepared to construct a corresponding Acceleration vs. Time
graph.
10
21. An automobile, which set the world record for acceleration, increased speed from rest to 96.0 km/hr in 3.07
seconds (2490 km/hr2). What distance was traveled by the time the final speed was achieved? (41 m)
22. The polar bear is an excellent swimmer, and it spends a large part of its time in the water. Suppose a polar
bear wants to swim from an ice flow to a particular point on the shore where it knows tasty seals gather. The
bear dives into the water and begins swimming with a speed of 2.60 m/s. By the time it arrives at the shore, its
speed has decreased to 2.20 m/s. If the polar bear’s swim takes exactly 9.00 min and it has a constant
deceleration, what is the distance traveled by the polar bear? (1296 m)
23. In a car accident involving a sports car, skid marks as long as 290.0 m were left by the car as it decelerated to
a complete stop. The police report cited the speed of the car before braking as being “in excess of 100 mph”
(161 km/hr). Suppose that it took 10.0 s for the car to stop. Estimate the speed of the car before the brakes
were applied. (58 m/s)
24. Peter Rosendahl rode his unicycle a distance of 100.0 m in 12.11 seconds. If Rosendahl started at rest, what
was the magnitude of his acceleration during his ride? (1.36 m/s2)
25. Suppose Mr. Rosendahl began riding the unicycle with a speed of 3.00 m/s and traveled a distance of 100.0
meters in 12.11 s. What would be the magnitude of his constant acceleration in this case? (0.876 m/s2)
26. The highest speed to be achieved by a standard nonracing sports car is 350.0 km/hr. Assuming that the car
accelerates at 4.00 m/s2, how long would this car take to reach its maximum speed if it is initially at rest? What
distance would the car travel during this time? (24.25 s, 1176 m)
27. The distance record for someone riding a motorcycle on its rear wheel without stopping is more that 320 km.
Suppose the rider in this unusual situation travels with an initial speed of 8.0 m/s before speeding up. The rider
then travels 40.0 m at a constant acceleration of 2.00 m/s2. What is the rider’s speed after the acceleration?
(14.9 m/s)
28. With a cruising speed of 2300 km/hr, the French supersonic passenger jet Concorde is the fastest commercial
airplane. Suppose the landing speed is 20.0 percent of the cruising speed. Over what distance does the plane
travel to a complete stop if its deceleration has a magnitude of 5.80 m/s 2? (1412 m)
29. The lightest car in the world was built in London and weighed less than 10 kg. Its maximum speed was 25.0
km/hr. Suppose the driver of this vehicle applies the brakes while the car is moving at its maximum speed.
The car stops after traveling 16.0 m. Calculate the magnitude of this deceleration. (-1.49 m/s2)
30. Rob Colley set a record in the dangerous sport of “pole-sitting” when he spent 42 days in a barrel at the top of a
flagpole with a height of 43 m. Suppose a friend wanting to deliver an ice-cream sandwich to Colley throws the
ice cream straight up with just enough speed to reach the barrel. How long does it take the ice-cream to reach
the barrel? (2.9 s)
31. Brian Berg of Iowa built a house of cards 4.88 m tall. Suppose Berg throws a ball from ground level straight up
so that the ball just passes the top of the card house with a speed of 2.00 m/s. Calculate the initial speed of the
ball. (10.0 m/s)
32. The Westin Stamford Hotel in Detroit is 228 m tall. If a worker on the roof drops a sandwich, how long does it
take the sandwich to hit the ground (neglecting air resistance)? How would air resistance affect the answer?
(6.75 s)
Use the Acceleration vs. Time graph shown below to answer the following:
33. If the velocity at t = 0 is 12 m/s, what is the velocity of the object at t = 2 seconds? At t = 4 seconds? (20 m/s,
28 m/s)
34. “Jerk” is the rate of change of acceleration with respect to time, a/t. What is the value for average jerk for t
= 0 to 2 seconds? For t = 4 to 6 seconds? (0 m/s3, -1 m/s3)
35. Construct the velocity vs. time graph for the motion shown:
36. Using the velocity vs. time graph you’ve constructed, what is the average acceleration for the eight seconds
shown? (3 m/s2)
Acceleration (m/s2)
Acceleration vs. Time
5
4
3
2
1
0
0
1
2
3
4
Time (s)
5
6
7
8