**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. (easy) Outline a procedure that would allow a student to determine the acceleration of a dragster on a straight track. Identify common measurement devices that would be needed. Assume that the dragster undergoes a uniform acceleration.

4. (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?

5. (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?

6. (moderate) A cart is at x=5m 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.

7. (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?

8. (OPTIONAL 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?

**PA Homeschooler Students: Prior to moving to the next assignment in the workflow, you must work through the following scenario in the AP Physics 1 Student Workbook. If you have mastered the concepts, you should find that the questions in the scenarios can be easily answered. If not, please take advantage of the additional practice found in the companion text.**

Click here to download Student Workbook.

Scenario 1I