PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
On a straight, level highway three independent pairs of cars move such that each pair will eventually pass one another. All motions occur along the same straight line. Consider the following information recorded at the same instant of clock time:
• Pair I – Car P is moving east at 35\,m\,s−1 and Car Q is moving west at 20\,m\,s−1. The cars are 4.0\,km apart.
• Pair II – Car R is moving east at 25\,m\,s−1 and Car S is moving east at 5.0\,m\,s−1, with Car R trailing. The cars are 1.5\,km apart.
• Pair III – Car T is moving west at 30\,m\,s−1 while Car U is at rest on the shoulder 0.80\,km directly ahead of Car T.
Assume the highway defines the +x axis toward the east.
Answer the following questions about the motion of each pair.
(a) For each pair, state whether the separation distance between the two cars is currently increasing, decreasing, or constant. Justify your answer using velocity information.
(b) Rank the three pairs (I, II, III) in order of decreasing magnitude of the rate at which the separation distance between the cars is changing at the instant described. Clearly indicate any ties in your ranking.
(c) For Pair II, determine the time required, after the instant described, for the faster car to draw even with the slower car. Show all reasoning.
(d) Without performing additional calculations, explain whether the ranking you provided in part (b) would change if all speeds were doubled while initial positions remained the same.