**Practice Problems: Kinematics**Click here to see the solutions.

1. (easy) How fast will an object (in motion along the x-axis) be moving at t = 10 s if it had a speed of 2 m/s at t = 0 and a constant acceleration of 2 m/s^{2}?

2. (easy) A car is rolling toward a cliff with an initial speed of 15 m/s. The maximum negative acceleration that the brakes can provide is -0.3 m/s^{2}. If the cliff is 350 m from the initial position of the car, will the car go over the cliff?

3. (moderate) Which would have the greatest effect on the displacement of an object that is accelerating uniformly in one-dimensional motion: doubling the initial velocity or doubling the time of the acceleration? Additionally, does the magnitude of the acceleration play any role in the difference of effect between these two parameters?

4. (moderate) Cart A moves with a uniform speed past point 1 on a straight track at 0.3 m/s. Cart B moves past point 1 at 0.1 m/s but is uniformly accelerating at 0.1 m/s^{2}. Point 2 is 1.0 m past point 1. Which cart gets to point 2 first?

5. (easy) A small ball is released from a window at t = 0. Assuming free-fall conditions, how far does it travel in 2.8 seconds? If the ball had more mass would it fall a greater distance?

6. (moderate) Three spheres are held at at various positions above a table. Sphere 1 is closest to the table, sphere 3 is furthest from the table. Assume all collisions with the table are perfectly elastic. That is, no energy is lost upon impact and the sphere returns to its initial height before it falls again as if it was dropped from rest. Consider motion up away from the table to be positive motion.

For questions A and B assume the following:

Sphere 1 initial height = 2.0 m

Sphere 2 initial height = 3.0 m

Sphere 3 initial height = 4.0 m

Sphere 1 is released from rest.

A. At what speed must sphere 2 be initially traveling upward if it first hits the table at the same time that sphere 1 hits the table for a second time?

B. At what speed must sphere 3 be initially traveling downward if it first hits the table at the same time that sphere 1 hits the table for the first time?

C. Now assume that the initial upward speed of sphere 2 is 1 m/s and the initial upward speed of sphere 3 is 2 m/s, determine the difference in initial heights of spheres 2 and 3 if they hit the table for the first time when sphere 1 hits the table for the sixth time. Sphere 1 is released from rest.

7. (easy) A cart is at x=5 m at time t=0. The cart accelerates at 4 m/s^{2}. If the speed of the cart at t=0 is 3 m/s, find the position of the cart at t= 2 s and also determine where the cart is when it reaches a speed of 5 m/s.

8. (moderate) A car moving at 20 m/s passes a street corner. The car maintains this speed even though the speed limit is 10 m/s. The police car that was sitting at the corner begins to chase the car by accelerating at 2 m/s^{2}. How long will it take for the police car to catch the speeder? How far from the corner is the catch-up point? How fast will the police car be traveling at that time?

9. (hard) Two spheres are rolling toward each other. At t = 0, sphere 1 is at x = 0 and has a speed of 10 m/s to the right while sphere 2 is moving 2 m/s to the left and has an initial position of x = 1000 m. Observations of the spheres show the following data:

-After 2 s, sphere 2 has picked up speed and is moving at 10 m/s to the left. This acceleration is maintained until the spheres collide.

-Sphere 1 is seen to have an acceleration of 2 m/s^{2} to the right. How fast will each sphere be traveling when they collide?

10. (moderate) This problem is a followup to one you saw in the previous presentation about cars at a red light:

Cars are lined up (with 5.0 m of distance between each car) at a red light. Assume

that each car is 4.6 m in length. When the light turns green, all cars accelerate at 1.22 m/s2 for 10.0 seconds, and then proceed at a constant speed. If the light stays green for 90.0 seconds, how many cars make it to the beginning of the intersection?

11. (moderate) Determine the distance between two steel spheres (after 1.4 s) dropped from a tower if the second sphere was dropped 0.5 seconds after the first. Assume free-fall and that the spheres are dropped from rest.

12. (hard) If a ball is tossed up (free-fall conditions) with an initial speed of 2.0 m/s does it spend more time in the top 0.1 m of the toss or the bottom 0.1 m of the toss?

13. (moderate) A model rocket enthusiast launches a rocket with a motion sensor in the launchpad. Assume y = 0 at the launchpad, that positive is up, and that the fuel mass is very small compared to the rocket body mass. Create qualitative y-t, v-t, and a-t graphs for an experiment that starts at lift off and ends when the rocket hits the Earth on the way back down. Assume free fall after the rocket fuel is used up.

**Please supplement these problems with those found in your companion text.**