Kinematics：練習題

A sprinter accelerates from rest to a speed of \(10.0\text{ m s}^{-1}\) in a time of \(4.0\text{ s}\). Assuming the acceleration is uniform, what is the distance covered by the sprinter during this time?

A particle moves in a straight line with uniform acceleration. It covers a distance of \(24.0\text{ m}\) in the first \(2.0\text{ s}\) interval and a distance of \(40.0\text{ m}\) in the next \(2.0\text{ s}\) interval. What is the acceleration of the particle?

A projectile is launched from point P with a velocity \(v\) at an angle \(\theta\) to the horizontal. It hits a target at the same horizontal level as P. If the time of flight is \(T\), which expression represents the maximum height \(h\) reached by the projectile?

Which of the following is equal to the area under a velocity–time graph for an object moving with non-uniform acceleration?

In an experiment to determine the acceleration of free fall \(g\), a steel ball is dropped from rest through two light gates connected to a digital timer. The ball passes through the first light gate at speed \(v_1\) and the second light gate at speed \(v_2\). The vertical distance between the two light gates is \(h\).
Which expression correctly gives \(g\)?

A displacement-time graph for a moving object is a straight line with a constant positive gradient. What physical quantity is represented by the gradient of this graph?

A train accelerates uniformly from rest at a rate of \(a\) for a time \(t_1\), then immediately decelerates uniformly at a rate of \(2a\) until it comes to rest at time \(t_2\). Determine the ratio of the time of acceleration \(t_1\) to the total time of motion \(t_2\).

A projectile is launched from ground level with speed \(u\) at an angle \(\theta\) above the horizontal. At time \(t\), its velocity vector is perpendicular to its initial velocity vector. Assuming air resistance is negligible, deduce an expression for the time \(t\) in terms of \(u\), \(g\), and \(\theta\).

A small stone is thrown vertically upwards from the edge of a cliff with an initial speed of \(12.0\text{ m s}^{-1}\). The stone eventually falls into the sea at the base of the cliff, which is a vertical distance of \(35.0\text{ m}\) below the point of release. Neglect air resistance. For this motion:

(a) Calculate the maximum height reached by the stone above the point of release.
(b) Determine the time taken for the stone to reach the surface of the sea from the moment it was thrown.
(c) Calculate the speed of the stone just before it hits the water surface.
(Take \(g = 9.81\text{ m s}^{-2}\))

A student uses a video camera to record the motion of an electric toy car moving along a straight horizontal track. The graph shows the variation with time \(t\) of the velocity \(v\) of the car over an interval of \(12.0\text{ s}\).

(a) State how the acceleration of the car at \(t = 2.0\text{ s}\) can be determined from the graph, and calculate its value.
(b) Determine the maximum displacement of the car from its initial position \(t = 0\).
(c) Determine the final displacement of the car at \(t = 12.0\text{ s}\).