How can you estimate the acceleration of a ball from a velocity versus time graph?

To estimate the acceleration of a ball from a velocity versus time graph, one looks at the slope of the graph. The slope of a velocity versus time graph represents acceleration because acceleration is defined as the rate of change of velocity over time. If the graph shows a straight line, the acceleration is constant and can be found by calculating the rise (change in velocity) divided by the run (change in time). For curves, the slope at any point represents the instantaneous acceleration. Thus, knowing how to find and interpret that slope is key to understanding the ball's acceleration.

The area under the graph represents displacement, which is separate from the concept of acceleration. While calculating total distance can be done, it does not directly relate to determining acceleration. Analyzing the curve may help in understanding when acceleration changes but does not provide a specific method for estimating acceleration itself. Therefore, focusing on the slope directly connects to the definition and calculation of acceleration.