# Problems: Kinematics in One Dimension

- A car accelerates from 12.0 m/s to 19.0 m/s in 3 seconds. What distance did it travel in this time?
- A car is traveling with a speed of 22 m/s. The brakes can produce a maximum deceleration of 8.0 m/s
^{2}. What is the minimum stopping distance for the car? - A jet aircraft requires 2.5 seconds of acceleration over a 94 m distance. What is the launch speed of the plane?
- A rock is dropped into a 100 m deep well. How long until the rock hits the bottom?
- A baseball is thrown upward with an initial speed of 35.0 m/s. What is its speed at
*t*= 2.00 s? - 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?
- 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/s
^{2})a) How long was it in the air? b) What is its final velocity? - A particle’s motion is described by its position at any given time
*t*.- Write down the definition of displacement, average velocity, and acceleration of an object moving in two dimensions.
- Derive the instantaneous velocity in terms of time and acceleration.
- Derive the position in terms of time, velocity, and acceleration.

- 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?
- 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?
- 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.
- An electron in a cathode ray tube accelerates from a speed v
_{1}to v_{2}over a distance d. How long does it take to travel this distance? If v_{1}= 2.0 x 10^{4}m/s, v_{2}= 6.0 x 10^{6}m/s and d = 150 cm, calculate the time to travel this distance. - 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/s
^{2}and L = 9.00 m, calculate the speed of the ball at the bottom of the plane. - 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/s
^{2}and L = 9.00 m, calculate the time required for the ball to reach at the bottom of the plane. - 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.

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