Displacement, Velocity, and Acceleration：練習問題

An object is dropped from rest from the top of a building of height \(h\). Assuming air resistance is negligible and the acceleration due to gravity is \(g\), which of the following expressions represents the time \(t\) it takes for the object to reach the ground?

The velocity-time graph of a toy car moving along a straight track is shown below. The car starts from rest at \(t = 0\), accelerates uniformly to a velocity of \(10\text{ m/s}\) in \(4\text{ s}\), maintains this velocity for \(6\text{ s}\), and then decelerates uniformly to a stop in \(2\text{ s}\). What is the total distance traveled by the car?

A ball is thrown vertically upward from the ground with an initial speed of \(v_0\). Neglecting air resistance, which of the following expressions represents the maximum height \(H\) reached by the ball?

A car is traveling at a constant speed of \(20\text{ m/s}\) when the driver sees a hazard and applies the brakes. If the reaction time of the driver is \(0.5\text{ s}\) and the car decelerates at a constant rate of \(5\text{ m/s}^2\), what is the total stopping distance of the car from the moment the hazard is seen?

A ball is thrown vertically upward with an initial velocity of \(15\text{ m/s}\). Assuming the acceleration due to gravity is \(g = 10\text{ m/s}^2\) and air resistance is negligible, what is the maximum height reached by the ball above its starting point?

A runner accelerates from rest to a velocity of \(8\text{ m/s}\) in \(4\text{ s}\) with constant acceleration. What is the total displacement of the runner during this time interval?

A position-time graph for a particle moving along a straight line shows a curve where the slope is steadily increasing. What can be concluded about the velocity and acceleration of the particle?

An object is dropped from a height of \(45\text{ m}\) above the ground. Neglecting air resistance and using \(g = 10\text{ m/s}^2\), how long does it take for the object to reach the ground?

A small object is released from rest at the top of a smooth inclined plane of length L. The object slides down the plane with a constant acceleration of \(2.0\text{ m/s}^2\).

(a) Calculate the time taken for the object to reach the bottom of the plane if \(L = 16\text{ m}\).
(b) Determine the speed of the object as it reaches the bottom of the plane.