Mechanics | Relativity Answers

A train started from rest and moved with constant acceleration. At one time it was traveling 20 m/s, and 170 m farther on it was traveling 46 m/s. Calculate (a) the acceleration, (b) the time required to travel the 170 m mentioned, (c) the time required to attain the speed of 20 m/s, and (d) the distance moved from rest to the time the train had a speed of 20 m/s.

To stop a car, first you require a certain reaction time to begin braking; then the car slows under the constant braking deceleration. Suppose that the total distance moved by your car during these two phases is 51.9 m when its initial speed is 78.3 km/h, and 23.6 m when its initial speed is 49.1 km/h. What are (a) your reaction time and (b) the magnitude of the deceleration?

In an arcade video game, a spot is programmed to move across the screen according to x = 8.79t - 0.658t^3, where x is the distance in centimeters measured from the left edge of the screen and t is time in seconds. When the spot reaches a screen edge, either at x = 0 or x = 15.0 cm, t is reset to 0 and the spot starts moving again according to x(t). (a) At what time after starting is the spot instantaneously at rest? (b) At what value of x does this occur? (c) What is the spot's acceleration when this occurs? (d) At what time t > 0 does the spot first reach an edge of the screen?

Two particles move along an x axis. The position of particle 1 is given by x = 9.00t^2 + 6.00t + 5.00 (in meters and seconds); the acceleration of particle 2 is given by a = -8.00t (in meters per seconds squared and seconds) and, at t = 0, its velocity is 20.0 m/s. When the velocities of the particles match, what is their velocity?

A basketball player grabbing a rebound jumps 76 cm vertically. How much total time (ascent and descent) does the player spend (a) in the top 13 cm of this jump and (b) in the bottom 13 cm? Do your results explain why such players seem to hang in the air at the top of a jump?

An object falls a distance h from rest. If it travels 0.55h in the last 1.00 s, find (a) the time and (b) the height of its fall.

A ball of moist clay falls 17.5 m to the ground. It is in contact with the ground for 19.0 ms before stopping. (a) What is the average acceleration of the ball during the time it is in contact with the ground? (Treat the ball as a particle.) (b) Is the average acceleration up or down?

A bolt is dropped from a bridge under construction, falling 95 m to the valley below the bridge. (a) How much time does it take to pass through the last 26 % of its fall? What is its speed (b) when it begins that last 26 % of its fall and (c) just before it reaches the ground?

A hoodlum throws a stone vertically downward with an initial speed of 13.0 m/s from the roof of a building, 40.0 m above the ground. (a) How long does it take the stone to reach the ground? (b) What is the speed of the stone at impact?

At a construction site a pipe wrench struck the ground with a speed of 27 m/s. (a) From what height was it inadvertently dropped? (b) How long was it falling?