Serway & Jewett — Motion in One Dimension: Problem 19

A glider of length \(\ell\) moves through a stationary photogate on an air track. A photogate (Fig. P2.19) is a device that measures the time interval \(\Delta t_d\) during which the glider blocks a beam of infrared light passing across the photogate. The ratio \(v_d = \ell / \Delta t_d\) is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant acceleration. (a) Argue for or against the idea that \(v_d\) is equal to the instantaneous velocity of the glider when it is halfway through the photogate in space. (b) Argue for or against the idea that \(v_d\) is equal to the instantaneous velocity of the glider when it is halfway through the photogate in time.