Practice Problems: Kinematics
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1. (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/s2. If the cliff is 350 m from the initial position of the car, will the car go over the cliff?
2. (easy) A cart is at x=5 m at time t=0. The cart accelerates at 4 m/s2. 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.
3. (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/s2. 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?
4. (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/s2 to the right.
How fast will each sphere be traveling when they collide?
Please supplement these problems with those found in your companion text.