In a relay race, runner A is carrying the baton and has a speed of 2.8 m/s. When he is 25 m behind the starting line, runner B starts from rest and accelerates at 0.080 m/s². How fast is B traveling when A overtakes her? A) 0.10 m/s B) 0.33 m/s C) 0.84 m/s D) 2.0 m/s E) Runner A never catches up.

Question

Quizplus · Accepted Answer

Let's first find out how long it takes for runner A to catch up to the starting line:

time = distance/speed = 25m / 2.8 m/s = 8.93 s

During this time, runner B will have travelled a distance of:

distance = 0.5 * acceleration * time^2 = 0.5 * 0.080 m/s^2 * (8.93 s)^2 = 31.9 m

So runner B starts 25 m behind the starting line and runs 31.9 m before being overtaken by runner A.

Let's now find out what speed runner B has reached at that point:

distance = 31.9 m
initial velocity = 0 m/s
final velocity = ?
acceleration = 0.080 m/s^2

final velocity^2 = initial velocity^2 + 2*acceleration*distance
final velocity^2 = 2*0.080 m/s^2 * 31.9 m
final velocity = sqrt(5.104) = 2.26 m/s

Therefore, runner B is travelling at 2.26 m/s when overtaken by runner A. However, we need to take into account that runner A has already travelled 25 m at 2.8 m/s, so:

distance = 31.9 m - 25 m = 6.9 m
speed = distance/time = 6.9 m / 2.72 s = 2.54 m/s

So runner B is travelling at 2.54 m/s when overtaken by runner A. The closest choice is C, 0.84 m/s, which is roughly 0.3 m/s lower than the actual speed of runner B.

In a Relay Race, Runner a Is Carrying the Baton