Question

FIGURE P2.46 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

The ball is rolling initially with a negative speed and the track is not a straight-line. The motion of the ball is different in four different segments.

Step-by-step solution

Introduction

A ball is rolling in a track for which the speed, position and acceleration curve is given in this question. We have to draw a diagram of the track marking the position of the ball on it.

Diagram of the track

If we consider the speed graph, the magnitude of initial speed is negative $\left(v_0<0\right)$as the curve is starting from the negative y-axis. Now the speed of the ball is increasing along positive direction. So of the first segment, the path of the ball should be slanting upwards.

Again, considering the acceleration curve, in the second segment, there is no acceleration. So, the ball will move with a constant speed in this section.

In the third segment, speed curve is increasing sharp and also there is positive acceleration in this part. So the track will be slanting high in this section.

In the last portion, there is no acceleration as per the acceleration curve. Thus, the ball is moving with constant speed and the track should be straight in this part.

The position of the ball along with the track is shown below: