Question

FIGURE P2.45 shows a set of kinematic graphs for a ball rolling on a track. All segments of the track are straight lines, but some may be tilted. Draw a picture of the track and also indicate the ball’s initial condition.

Short answer

A ball rolling in a track with zero initial speed is mentioned here. The position, acceleration and speed curve is given from which we can draw a picture of its track and also its position.

Step-by-step solution

Introduction

A ball is rolling in a track with a zero initial speed. Further moving in three different segments, the ball is moving with constant speed and accelerating further.

Pictorial representation

Referring to the speed-time graph, the ball has a zero initial speed in the initial segment. Then it is rolling with an acceleration for which the track should be slanting downwards and the ball will be rolling fast gradually.

In the second segment, there is no acceleration of the ball according to the acceleration graph. So the ball is rolling in a straight-line.

In the third segment, the magnitude of acceleration is greater than the acceleration it had previously. In the position curve, we can see the slope is largest in this portion. So the track is steeper than before in this segment.

The position of the ball initially and the track in which it is rolling are shown here: