Question

During a track event two runners, Bob, and Jim, round the last turn and head into the final stretch with Bob a distance d in front of Jim. They are both running with the same velocity v 0 . When the finish line is a distance s away from Jim, Jim accelerates at a constant a J until he catches up to Bob and passes him. Jim then continues at a constant speed until he reaches the finish line.

a) How long did it take Jim to catch Bob?

b) How far did Jim still have to run when he just caught up to Bob?

c) How long did Jim take to reach the finish line after he just caught up to Bob? Bob starts to accelerate at a constant a B at the exact moment that Jim catches up to him, and accelerates all the way to the finish line and crosses the line exactly when Jim does. Assume Bob’s acceleration is constant.

d) What is Bob’s acceleration?

e) What is Bob’s velocity at the finish line? Who is running faster?

Answer 1

(a)

Relative distance between Bob and Jim is d. Calculate the relative speed between them and find the time

(b)

Find the distance traveled by Jim and subtract it from the initial distance from finish line.

(c)

Find the velocity attained by Jim when he caught up with Bob. Speed of Jim remains constant after that. Distance left to run is taken from part b.

(d)

Time taken by Bob is equal to that of Jim.

(e)