Two motorcyclists start simultaneously from towns X and Y
PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Two motorcyclists start simultaneously from towns X and Y, which are 120km apart on a straight highway. Motorcyclist A leaves town X with an initial speed of 20m s−1 and accelerates uniformly at 0.2m s−2. Motorcyclist B leaves town Y with an initial speed of 25m s−1 but decelerates uniformly at 0.1m s−2 as he approaches X.
(a) Set up the necessary equations of motion for both riders, choosing a single origin and positive direction, and hence obtain an equation whose solution gives the time at which they meet.
(b) Solve the equation to find the time of meeting.
(c) Calculate the distance of the meeting point from town X.
(d) Determine the speed of each motorcyclist at the instant they cross each other.