Kinematics：練習題

A sprinter accelerates from rest to a velocity of \(12\text{ m s}^{-1}\) in a time of \(3.0\text{ s}\). What is the average acceleration of the sprinter during this time interval?

A projectile is launched from horizontal ground with an initial velocity of \(25\text{ m s}^{-1}\) at an angle of \(30^{\circ}\) to the horizontal. Neglecting air resistance, what is the time of flight before the projectile returns to the ground?

Two stones, X and Y, are thrown from the top of a cliff. Stone X is thrown vertically upwards with speed \(u\) and stone Y is thrown vertically downwards with the same speed \(u\). Neglecting air resistance, which statement is correct regarding the speeds of the stones when they hit the shore below?

Which expression correctly defines the average speed of an object during a journey?

A car is traveling along a straight road at a speed of \(25\text{ m s}^{-1}\). The driver applies the brakes, resulting in a constant deceleration of \(4.0\text{ m s}^{-2}\). What is the distance traveled by the car from the moment the brakes are applied until it comes to rest?

Express the SI unit of acceleration in terms of SI base units.

The motion of an object is represented by the velocity–time graph shown. Determine the total displacement of the object during the \(12\text{ s}\) interval.

A train starts from rest and accelerates uniformly at \(0.50\text{ m s}^{-2}\) for \(20\text{ s}\). It then travels at this constant velocity for \(30\text{ s}\) before decelerating uniformly to rest in a further \(10\text{ s}\). Calculate the total distance traveled by the train.

(a) Define displacement.
(b) A cyclist starts from rest and moves with a constant acceleration of \(1.2\text{ m s}^{-2}\) along a straight horizontal road for a time of \(5.0\text{ s}\).
(i) Calculate the velocity of the cyclist at the end of the \(5.0\text{ s}\) period.
(ii) Calculate the distance traveled by the cyclist during these \(5.0\text{ s}\).
(c) State the feature of a velocity–time graph that represents the acceleration of the cyclist.

A car is traveling at a constant velocity of \(12\text{ m s}^{-1}\) along a straight road. The driver sees a hazard and applies the brakes, causing the car to decelerate uniformly to rest over a distance of \(30\text{ m}\).
(a) Show that the magnitude of the deceleration is \(2.4\text{ m s}^{-2}\).
(b) Calculate the time taken for the car to come to rest after the brakes are applied.
(c) The driver has a reaction time of \(0.45\text{ s}\). Calculate the total distance covered by the car from the moment the driver sees the hazard until the car stops.