PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A cyclist rides north–south on a straight road. The velocity v(t), in kilometres per hour, is described verbally as follows.
• From t=0 min to t=6 min, the cyclist’s velocity decreases linearly from 10kmh−1 northward to 0.
• Between t=6 min and t=10 min, the cyclist remains stopped.
• From t=10 min to t=14 min, the cyclist accelerates uniformly, reaching 8kmh−1 southward at t=14 min.
Ignore any turning radius; the rider simply reverses direction at rest.
(a) On the axes of your answer booklet, sketch a qualitative graph of v(t) for 0≤t≤14 minutes. Label intercepts and significant function values clearly.
(b) For each of the three sub-intervals described, state the constant or functional form of the acceleration in kmh−2. Justify your answers briefly.
(c) Calculate the cyclist’s net displacement (in kilometres, north positive) for the entire 14–minute ride.
(d) Calculate the total distance the cyclist travels over the same period and compare it with the magnitude of the displacement. Provide a brief explanation of any difference.
(e) Identify the exact clock time (to the nearest minute) at which the cyclist is farthest north of the starting point. Support your answer with reasoning based on the velocity graph.