PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Two cyclists, P and Q, begin riding at time t=0 (minutes) and finish at t=5 minutes along level ground. Their forward speeds (in meters per minute) vary with time as follows:
• Cyclist P rides at a constant 4 m/min for the first 3 minutes, then decelerates linearly to 2 m/min at t=5.
• Cyclist Q rides at a steady 3 m/min for the entire 5 minutes.
Assume each cyclist’s direction of travel remains fixed throughout.
(a) Sketch qualitative graphs of the speed functions vP(t) and vQ(t) on 0≤t≤5. Clearly label speeds and key times.
(b) Compute the exact distance traveled by each cyclist over the 5-minute interval. Show how geometric areas under the speed graphs lead to your results.
(c) State which cyclist covers the greater distance and by how many meters. Justify your answer based on part (b).