At 8:00 AM a truck departs on a straight freeway and travels east at a constant speed of
PHYSICS · Multi-part · CBSE · Physics · Motion in a Straight Line · Motion in a Straight Line
Problem
At 8:00 AM a truck departs x=0 on a straight freeway and travels east at a constant speed of 20m/s. Five minutes later (300s) a sports car leaves the same point, starting from rest and accelerating eastward at a constant rate of 2m/s2. The motions continue for several minutes. Let t be the number of seconds after 8:00 AM.
(1) Part 1: For t≥0 write an expression for the truck’s position xT(t) in meters. For t≥300 write an expression for the car’s position xC(t). Clearly indicate the domain of each expression.
(2) Part 2: Determine the time (in seconds after 8:00 AM) at which the car first reaches the truck. Give your answer to the nearest tenth of a second and justify that any other solution is extraneous for this context.
(3) Part 3: Compute the distance east of the origin at which the meeting in part (b) occurs.
(4) Part 4: Find the speed of the car at the instant it reaches the truck. Comment on how this speed compares to the truck’s speed.