Kinematics Problems
1. A jet airliner starts from rest at the end of a runway and acquires its take-off speed of 80.0 m/s in 45.0 seconds. Find a) its acceleration, b) the displacement after 45.0 seconds, c) the instantaneous speed at the end of 25.0 seconds.
2. Starting from rest on a launching pad, a rocket acquires a vertical velocity
of 145.0 m/s. in 12.0 seconds. Find the acceleration, and the displacement during the 12.0 seconds. (12.1 m/s/s, 871 m)
3. Starting from rest at the end of a runway, a jet passenger plane acquires its take-off speed of 85.0 m/s in 48.0 seconds. Find a) the acceleration, and b) the displacement.
c) Find the displacement in the first 10.0 seconds.
4. A man on a motorcycle starts from rest and acquires an instantaneous velocity
of 30.0 m/s in a distance of 120. m. Find a) the acceleration, and b) the time it took to
travel 120. m. (3.75 m/s/s, 8 sec)
5. A car moving along a level road increases its speed uniformly from 16.0 m/s
to 32.0 m/s in 10.0 seconds. a) What is the car’s acceleration? b) What is the car’s average speed during the 10.0 second interval? c) What was the displacement of the car during the acceleration? (1.60 m/s/s, 24 m/s, 240 m)
6. A ball initially at rest rolls down a hill with an acceleration of 3.30 m/s/s. a) What is its displacement after 7.50 seconds? b) What would be the displacement if it had started at 4.00 m/s rather than from rest. c) Sketch a position vs time graph, and a velocity vs time graph for both situations. Indicate on each graph how to find the displacement
at 7.50 seconds.
7. A boy sliding down a hill accelerates at 1.40 m/s/s. If he started from rest, in what distance would he reach a speed of 7.00 m/s?
8. A plane, starting from rest at one end of a runway, undergoes a constant acceleration of 1.60 m/s/s for a distance of 1600 m before takeoff. a) What is its speed before takeoff? b) What is the time required for takeoff? (71.6 m/s, 44.8 sec)
9. A passenger car starting from rest has an acceleration of 1.80 m/s/s for 12.0 seconds. After 5.00 seconds at the speed acquired, the brakes are applied bringing the car to rest in an additional time of 10.0 seconds. Find a) the constant speed acquired, b) the acceleration during the time the brakes are applied., and c) the total distance traveled.
d) Sketch a velocity vs time graph for the car for the entire time interval. Use the graph to calculate the total distance traveled.
10. A freight train with a speed of 12.0 m/s at the top of a long grade acquires a speed of 88.0 m/s when it reaches the bottom 4 min and 36 seconds later. Assuming constant acceleration, find a) the acceleration, and b) the total distance traveled.
11. A car starts from rest and maintains a uniform acceleration of 0.150 m/s/s for a distance of 2.00 km. Find a) its final speed, and b) its time of travel.
12. A man driving a truck at a constant speed of 25.0 m/s suddenly applies the brakes, bringing the truck to a stop in 5.00 seconds. Find a) the acceleration, b) the distance traveled, c) the speed at the end of 3.00 seconds, and d) the distance traveled during these 3.00 seconds.
13. A plane initially at rest is catapulted into the air at a speed of 55.0 m/s in
2.20 seconds. Calculate a) the acceleration, and b) the length of the catapult.
14. A jet plane is catapulted into the air with a speed of 62.0 m/s in 2.80 seconds. Calculate a) the acceleration, and b) the length of the catapult. (22.14 m/s/s, 86.8 m)
15. A boy drops a stone in a well and finds it takes 2.60 seconds to hit the water.
A) How deep is the well, and b) with what speed does the stone hit the water?
16. A sandbag, dropped as ballast from a balloon, hits the ground with a speed
of 147.0 m/s. a) How high is the balloon, and b) how long is the sandbag in the air?
17. Working on a tall building a workman accidentally drops a hammer. If it
takes 7.60 seconds to reach the ground, a) how high was the man working, and b) with what speed does it hit the ground? (283 m above the ground, -74.5 m/s)
18. A penny dropped from the roof of a building takes 6.30 seconds to strike the ground. How high is the roof?
19. A flowerpot falls from a window sill 25.0 m above the sidewalk. A) How fast is the flowerpot moving when it strikes the ground? How much time does a passerby on the sidewalk below have to move out of the way before the flower pot hits the ground?
20. A stone is dropped from a bridge 60.0 m above the water. a) how long is the stone in the air, and b) with what speed does it hit the water? (3.50 sec, -34.3 m/s)
21. A physics student throws a softball straight up into the air. Her friend has a stopwatch and determines the ball was in the air for a total of 3.56 s. a) With what speed was it thrown? b) How high did it rise?
22. An arrow, shot straight upward, reaches a height of 99.2 m. a) With what velocity does it leave the bow, and b) how long is it in the air? (44.1 m/s, 9.00 sec)
23. A ball thrown straight upward reaches a height of 80.0 m. Calculate a) the time to reach the highest point, and b) the speed of the ball upon arrival at the point of origin.
24. A stone is projected straight upward with an initial velocity of 45.0 m/s. Find a) how long the ball is in the air, and b) how high it rises. (9.18 sec, 103 m)
25. A boy standing on a bridge 150 m above the canyon floor throws a stone downward with a speed of 20.0 m/s. a) With what velocity will it hit the ground, and b) how long will it take to descend? (-57.8 m/s, 3.86 sec)
26. While standing on a bridge 80.0 m above the water, a boy throws a stone straight downward with a velocity of 15.0 m/s. a) With what speed will the stone hit the water, and b) how long will it take to descend?
27. A ball is thrown straight upward with a speed of 19.60 m/s. Find a) the height to which it rises, b) the total time it is in the air, c) its height above the ground at the end of 1.50 seconds, and d) its velocity at the end of 1.50 seconds.
28. A boy standing on a bridge throws a stone vertically upward with a velocity
of 29.4 m/s. Find a) the velocity and b) the position of the stone at the end
of 7.00 seconds.
29. A stone is thrown vertically upward with a velocity of 45.0 m/s. At the end
of 10.0 seconds a) where is the stone located, and b) with what speed is it moving?
30. A water rocket starts from rest and rises straight up with an acceleration
of 5.00 m/s/s until it runs out of water 2.50 seconds later. a) If it continues to rise until its speed is zero, what will be its maximum height? b) Sketch a velocity vs time graph for the rocket. Use the graph to determine the maximum height form part a.