Question

A ball rolls along the smooth track shown in FIGURE P2.43. Each segment of the track is straight, and the ball passes smoothly from one segment to the next without changing speed or leaving the track. Draw three vertically stacked graphs showing position, velocity, and acceleration versus time. Each graph should have the same time axis, and the proportions of the graph should be qualitatively correct. Assume that the ball has enough speed to reach the top.

Short answer

Three graphs showing position, velocity, and acceleration versus time.

Step-by-step solution

Given information

Every segment of the track is straight, and the ball passes smoothly from one segment to the next without changing speed or leaving the track.

Graph of position versus time.

The graph of position versus time of the given situation is shown below.

In the first and third segments position increases linearly and in the second segment it increases parabolically.

Graph of velocity versus time.

The graph of velocity versus time of the given situation is given below.

A ball passes smoothly in first and third segments, the velocity in the first and third segments is constant and as the ball going up against the gravity, velocity decreases linearly with time in the second segment.

Graph of acceleration versus time.

The graph of acceleration versus time is shown below.

As the velocity is constant in the first and third segments, the acceleration is zero in those segments. In the second segment, as the velocity is decreasing linearly, that is, the graph of velocity vs time has a negative slope, the acceleration has a constant negative value.