A ball is tossed with enough speed straight up so that it is in the air several seconds. Assume upward direction is positive and downward is negative.What is the acceleration of the ball during any of these time intervals? What is the acceleration of the ball at the moment the ball has zero velocity?
To determine the acceleration of the ball during any time interval, you need to consider the forces acting on the ball.
During the upward motion, the only force acting on the ball is the force of gravity, which is directed downward. Therefore, the acceleration during this interval is equal to the acceleration due to gravity, typically denoted as "g," which is approximately 9.8 m/s^2.
When the ball reaches its highest point and starts descending, the force of gravity continues to act on the ball, but now in the downward direction. Thus, the acceleration during this interval remains equal to the acceleration due to gravity, which is -9.8 m/s^2, considering the negative sign for the downward direction.
At the moment the ball has zero velocity, it is at its highest or lowest point. Therefore, when the ball reaches its highest point during upward motion or its lowest point during downward motion, the velocity becomes zero momentarily. At this instant, the direction of the velocity is changing from upward to downward, or vice versa. It is important to note that while the velocity is zero, the acceleration due to gravity is still acting on the ball and remains constant at -9.8 m/s^2.
So, in summary:
- During the upward motion: acceleration = +9.8 m/s^2 (upward)
- During the downward motion: acceleration = -9.8 m/s^2 (downward)
- At the moment the ball has zero velocity: acceleration = -9.8 m/s^2 (due to gravity)