Question

Draw position, velocity, and acceleration graphs for the ball shown in FIGURE P2.44. See Problem 43 for more information.

Short answer

Initially, the ball is stationary at a maximum position resulting in zero velocity. The position-time graph shows that with increasing time the ball is coming down from its maximum position to minimum position and then follows the parabolic path. The velocity of the ball increases in the negative direction becomes maximum and then decreases with increasing time. From the acceleration-time graph, it can be observed that the acceleration has a constant negative value initially and it goes from negative to a positive constant value as the ball reaches the minimum position in the given diagram.

Step-by-step solution

Given information

The given figure is

Position-versus-time graph

Let s be the distance along the track measured from the left and t be the time.

The graph of position-versus-time is shown below

Velocity-versus-time graph

Let $v_s$be the velocity of the ball. The graph of velocity-versus-time for the given situation is shown below

Acceleration-versus-time graph

Let $a_s$be the acceleration of the ball. As the angle of inclination is the same, the magnitude of the acceleration is the same on all tracks. The graph of acceleration-versus-time for the given situation is shown below