Linear motion：練習問題

A ball is thrown vertically upwards with an initial speed of \(15.0\, \text{m s}^{-1}\). Neglecting air resistance, what is the total time the ball remains in the air before returning to its starting height? (Take \(g = 9.81\, \text{m s}^{-2}\))

A vehicle is travelling at a constant speed \(v\). The driver sees a hazard and applies the brakes after a reaction time \(t_r\). The vehicle then decelerates uniformly at a rate \(a\) until it stops. What is the expression for the total stopping distance \(d\)?

A car travelling at \(20\, \text{m s}^{-1}\) decelarates uniformly to rest over a distance of \(40\, \text{m}\). Calculate the magnitude of the deceleration of the car.

A ball is projected horizontally from the top of a tower with speed \(v\). At the same instant, another ball is dropped from rest from the same height. If air resistance is negligible, which of the following is true?

A stone is thrown vertically upwards from the edge of a cliff of height \(H\) with an initial velocity \(u\). It reaches the base of the cliff after a time \(T\). Which equation correctly relates \(H\), \(u\), and \(T\)? (Take downwards as positive)

A car is travelling at a constant speed of \( 30\text{ m s}^{-1} \) when the driver sees a hazard. If the driver's reaction time is \( 0.60\text{ s} \) and the car decelerates at a constant rate of \( 5.0\text{ m s}^{-2} \), determine the total stopping distance of the vehicle.

A ball is dropped from a height \( H \) onto a hard floor. After the first bounce, it reaches a maximum height of \( 0.64H \). Calculate the ratio of the speed of the ball immediately after the bounce to the speed immediately before the bounce, and explain the energy transformation involved.

A toy rocket is fired vertically upwards. Its engine provides a constant upward acceleration of \( 4.0\text{ m s}^{-2} \) for the first \( 5.0\text{ s} \), after which the engine cuts out. Calculate the maximum height reached by the rocket above its launch point, assuming \( g = 9.81\text{ m s}^{-2} \) and neglecting air resistance.

A stone is thrown vertically upwards from the edge of a cliff with an initial speed of \( 15 \text{ m s}^{-1} \). The cliff is \( 40 \text{ m} \) high. Ignoring air resistance:
(a) Calculate the maximum height reached by the stone above the cliff top.
(b) Calculate the time taken for the stone to reach the base of the cliff from the moment it was thrown.
(c) Determine the velocity with which the stone hits the ground at the base of the cliff.
(d) State and explain how the time calculated in (b) would change if a significantly heavier stone were used.

A car is traveling at \( 30 \text{ m s}^{-1} \) on a level road. The driver sees a hazard and applies the brakes. The driver's reaction time is \( 0.65 \text{ s} \) and the car decelerates at a constant rate of \( 6.5 \text{ m s}^{-2} \).
(a) Define thinking distance and braking distance.
(b) Calculate the total stopping distance for this car.
(c) Discuss how the stopping distance would change if the car were traveling on a wet road, referring to the physical factors involved.