Question

whipple remembers hearing that the velocity is the distance divided by the time. he is curious to test if this simple statement is correct. to do so, he compares the final velocity of the tennis - ball with the change in height divided by the change in time. he runs the experiment several times, comparing the final velocity with the change in height divided by the change in time. whipple concludes, from his observations and some thought, that: - this simple relationship, v = δy/δt, works because the average velocity and the instantaneous velocities are always equal. - the quantity δy/δt represents the average velocity which is only equal to the instantaneous velocity in the case where the velocity is a constant. the correct relationship for the instantaneous velocity is v = lim(δt→0) δy/δt = dy/dt. - this simple relationship, v = δy/δt, is correct since the velocity is the slope of the displacement vs. time plot and the slope of a curve is simply the rise over the run. - this simple relationship, v = δy/δt, is valid only when the ball does not change direction, such as traveling upward and then downward.

Explanation:

The quantity $\Delta y/\Delta t$ represents average velocity. Instantaneous velocity is the limit of average velocity as $\Delta t$ approaches 0, i.e., $v = \lim_{\Delta t
ightarrow0}\frac{\Delta y}{\Delta t}=\frac{dy}{dt}$. Average velocity equals instantaneous velocity only when velocity is constant.

Answer:

The quantity $\Delta y/\Delta t$ represents the average velocity which is only equal to the instantaneous velocity in the case where the velocity is a constant. The correct relationship for the instantaneous velocity is $v=\lim_{\Delta t
ightarrow0}\frac{\Delta y}{\Delta t}=\frac{dy}{dt}$