Displacement, Velocity & Acceleration (College Board AP® Physics 1: Algebra-Based): Exam Questions

Figure 1

A long track, inclined at an angle to the horizontal, has small speed bumps on it. The bumps are evenly spaced a distance apart, as shown in Figure 1. The track is actually much longer than shown, with over 100 bumps. A cart of mass is released from rest at the top of the track. A student notices that after reaching the 40th bump, the cart's average speed between successive bumps no longer increases, reaching a maximum value . This means the time taken to move from one bump to the next becomes constant.

Consider the cart's motion between bump 41 and bump 44.

i) On the axes provided in Figure 2, sketch a graph of the cart's velocity as a function of time from the moment it reaches bump 41 until it reaches bump 44.

ii) On your graph, draw and label a line for the maximum average speed for the same time interval.

Figure 2

Derive an expression for the time taken for the cart to travel between two successive bumps. Write your expression in terms of , , , and physical constants as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.