PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
The velocity of a cyclist moving along a straight, level road is modeled as follows. For 0≤t≤4 seconds, the velocity increases linearly from 0 m/s at t=0 to 12 m/s at t=4. For 4<t≤8 seconds, the velocity decreases linearly to 4 m/s at t=8.
(a) Determine the cyclist’s average velocity on the interval 0≤t≤8 seconds. Show your reasoning and include units.
(b) Without further calculation, explain why the average velocity found in part (a) must lie between 4 m/s and 12 m/s.
(c) Calculate the average acceleration on 0≤t≤4 and on 4<t≤8, stating the units for each.
(d) Discuss the relationship between the instantaneous acceleration at t=4 seconds and the average accelerations found in part (c).