A student standing on level ground throws a tennis ball straight upward. A motion sensor records the vertical component of the ball’s velocity as a function of time. The sensor output can be described verbally as follows:
• At the instant of release, t=0 s, the velocity is +20m/s.
• Thereafter, the graph is a straight line that slopes downward at a constant rate of 9.8m/s2.
• The line crosses the time axis at t=2.0 s, then continues with negative values until the ball returns to the student’s hand at t=4.0 s.
Answer the following questions about the motion, using only the qualitative information provided in the description of the graph.
(a) Describe how the sign and constant magnitude of the slope of the velocity–time graph relate to the physical quantity called acceleration for the ball throughout the motion.
(b) Using the idea of the area under a velocity–time curve, explain why the ball’s vertical displacement between t=0 s and t=2.0 s is positive even though its instantaneous velocity reaches zero at t=2.0 s.
(c) Compare the magnitudes of the ball’s velocity at release (t=0 s) and just before it is caught (t=4.0 s). Provide a qualitative explanation for any similarity or difference you identify.