Question

An object starts linear motion with a velocity ‘u’ and under uniform acceleration ‘a’, it acquires a velocity ‘v’ in time ‘t’. Draw its velocity-time graph. From this graph, derive the position-time relation and position-velocity relation.

Answer 1

To draw the velocity-time graph, find the gradient of the position-time graph. The position-time relation can be derived by finding the area under the velocity-time graph. The position-velocity relation can be derived by finding the area under the acceleration-time graph.

Step-by-step explanation:

To draw the velocity-time graph, we know that the gradient of the position-time graph gives the velocity, so the graph will be a straight line.

The acceleration-time graph can be derived by finding the gradient of the velocity-time graph.

The position-time relation can be derived by finding the area under the velocity-time graph. Since the velocity-time graph is a straight line, the area will be a triangle, and the position-time graph will be a curve.

The position-velocity relation can be derived by finding the area under the acceleration-time graph.

Since the acceleration-time graph is a straight line, the area will be a trapezium, and the position-velocity graph will be a curve.