Question

A cylinder is given a push and then rolls up an inclined plane. If the origin is the starting point, sketch the position, velocity, and acceleration of the cylinder vs. time as it goes up and then down the plane.

Short answer

The cylinder is rolling, reaching a maximum height, and then returning to rest.

Step-by-step solution

Position versus Time

The position vs. time sketch is given below,

The body gains height from t = 0 to t = t s. At t, it reaches its maximum height.

The cylinder is attracted back to the earth due to gravitational force; hence it falls back and comes back to the same position from time t s to 2t s.

Velocity versus time graph

Initially, the velocity of the cylinder decreases as it climbs up, so there is a pull of gravitational force. When it reaches time t, the velocity becomes zero.

After which, it suddenly falls.

This falling is due to gravitational acceleration.

Figure: Velocity versus time graph

Similarly, to draw acceleration versus time graph.

When a cylinder rolls up an inclined surface, it suffers a negative acceleration.

The acceleration will be positive with a magnitude as it rolls down the hill.

The graph of acceleration vs. time is shown below.

Figure: Acceleration versus time graph

Hence, this graph mentions the motion of a cylinder rolling up and coming back.