The velocity (in meters per second) of a cyclist traveling along a straight road for…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
The velocity v (in meters per second) of a cyclist traveling along a straight road for 0≤t≤16 seconds is modeled by a piecewise-linear function described below:
• From t=0 to t=5, v increases linearly from 0 to 8.
• From t=5 to t=9, v remains constant at 8.
• From t=9 to t=12, v decreases linearly to −4.
• From t=12 to t=14, v remains constant at −4.
• From t=14 to t=16, v increases linearly back to 0.
Negative velocity indicates motion opposite the initial direction.
(1) Compute the cyclist’s net displacement over the interval 0≤t≤16. Show all work, including geometric reasoning for each subinterval.
(2) Compute the total distance traveled over the same time interval. Clearly indicate how regions below the t-axis are treated in your calculation.
(3) Determine the average velocity of the cyclist on 0≤t≤16. Express units clearly and justify your computation.
(4) Identify all time intervals during which the cyclist is moving opposite the initial direction. Explain how the sign of the definite integral on those intervals supports your conclusion.