One athlete in a race running on a long, straight track with a constant speed v1

Question

One athlete in a race running on a long, straight track with a constant speed v1 is a distance d behind a second athlete running with a constant speed v2.

(a) Under what circumstances is the first athlete able to overtake the second athlete?

(b) Find the time t it takes the first athlete to overtake the second athlete, in terms of d, v1, and v2.

(c) At what minimum distance d2 from the leading athlete must the finish line be located so that the trailing athlete can at least tie for the first place? Express d2 in terms of d, v1, and v2 by using the result of part (b).

Explanation / Answer

a) first athlete can overtake the second one only if

v1 is greater than v2

v1 > v2

b ) the relative velocity between the athletes is

v2 - v2

Distance between them is = d

The time taken to overtake t = distance / velocity

t = d / ( v1 - v2 )

c ) for the first athlete to just overtake second at the finish line, the first should be at least d2 distance from finish line.

d2 = t × v2

= d × v2 / (v1 -v2 )

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