# Problems: Kinematics in One Dimension

1. A car accelerates from 12.0 m/s to 19.0 m/s in 3 seconds. What distance did it travel in this time?
2. A car is traveling with a speed of 22 m/s. The brakes can produce a maximum deceleration of 8.0 m/s2. What is the minimum stopping distance for the car?
3. A jet aircraft requires 2.5 seconds of acceleration over a 94 m distance. What is the launch speed of the plane?
4. A rock is dropped into a 100 m deep well. How long until the rock hits the bottom?
5. A baseball is thrown upward with an initial speed of 35.0 m/s. What is its speed at t = 2.00 s?
6. Suppose you are visiting a planet in a distant part of the galaxy. To determine the acceleration due to gravity on the planet, you drop a rock from a height of 55 m. The rock strikes the ground 1.9 s later. How many times greater is the acceleration due to gravity on this planet than it is on earth?
7. You are on a 5 m high roof and throw a ball upwards at 10 m/s. It lands on the ground below you. (Use g=10 m/s2 )a) How long was it in the air? b) What is its final velocity?
8. A particle’s motion is described by its position at any given time t.
1. Write down the definition of displacement, average velocity, and acceleration of an object moving in two dimensions.
2. Derive the instantaneous velocity in terms of time and acceleration.
3. Derive the position in terms of time, velocity, and acceleration.
9. A person walks first at a constant speed v along a straight line from point A to point B and then back along the line from B to A at a constant speed v/2. What is her average speed over the entire trip?
10. A superball traveling with a speed 3v bounces off a brick wall and rebounds with a speed 2v. A high speed camera records this event. If the ball is in contact with the wall for a time t, what is the average acceleration of the ball during this interval?
11. Jules Verne in 1865 suggested sending people to the moon by firing a space capsule from a cannon with a barrel of length L with a launch speed v. What would have been the acceleration experienced by the space travelers? If L = 220 m and v = 10.97 km/s, what is the value of this acceleration.
12. An electron in a cathode ray tube accelerates from a speed v1 to v2 over a distance d. How long does it take to travel this distance? If v1 = 2.0 x 104 m/s, v2 = 6.0 x 106 m/s and d = 150 cm, calculate the time to travel this distance.
13. A ball starts from rest and moves with an acceleration a while moving down an incline plane of length L. What is the speed of the ball at the bottom of the plane? If a = 0.500 m/s2 and L = 9.00 m, calculate the speed of the ball at the bottom of the plane.
14. A ball starts from rest and moves with an acceleration a while moving down an incline plane of length L. How long does it take to roll down the plane? If a = 0.500 m/s2 and L = 9.00 m, calculate the time required for the ball to reach at the bottom of the plane.
15. A woman is reported to have fallen a distance h from top floor of a building, landing on a metal ventilator box, which she crushed to a depth d. She suffered only minor injuries. Neglecting air resistance, determine her speed just before contact with the ventilator. If h = 44.0 m and d = 45.0 cm, calculate her speed just before contact with the ventilator.