Graphical analysis of motion：練習問題

The displacement-time graph of a moving toy car is shown in the diagram. What is the velocity of the car during the first \(6.0\text{ s}\)?

The velocity-time graph represents the motion of an electric cart moving along a straight track over a period of \(12\text{ s}\). What is the total displacement of the cart at \(t = 12\text{ s}\)?

A ball is thrown vertically upwards and eventually returns to the starting point. Describe the shape of its velocity-time graph from the moment it is released until it reaching its maximum height, assuming upward is positive and air resistance is negligible.

Compare the acceleration of two objects, A and B, if the velocity-time graph for A is a straight line rising from \(0\) to \(10\text{ m/s}\) in \(2\text{ s}\), and for B it is a straight line rising from \(0\) to \(20\text{ m/s}\) in \(5\text{ s}\).

Sketch the shape of a velocity-time graph for an object that is dropped from a significant height and eventually reaches terminal velocity, taking air resistance into account.

A lift moves upwards. It starts from rest and its velocity increases at a constant rate for \(4\text{ s}\) until it reaches \(2\text{ m/s}\). It travels at this velocity for \(10\text{ s}\) and then slows down at a constant rate, coming to rest in a further \(2\text{ s}\).
(a) Sketch the velocity-time graph.
(b) From the graph, calculate the height the lift has risen.
(c) Calculate the average speed of the lift for the whole journey.

Two cars, A and B, start from the same point. Car A moves with a constant velocity of \(20\text{ m/s}\). Car B starts from rest and accelerates at \(4\text{ m/s}^2\).
(a) Draw the velocity-time graphs for both cars on the same axes.
(b) At what time \(t\) will Car B catch up with Car A?
(c) Calculate the distance travelled by both cars when Car B catches Car A.