What should your acceleration be if you are to catch up by the finish line?

Question

After 35 min of running, at the 9 km point in a 10 km race, you find yourself 100 m behind the leader

and moving at the same speed. What should your acceleration be if you are to catch up by the finish

line? Assume that the leader maintains constant speed.

Answer 1

Hi Mengyuan L.

Write your equations for distance for each runner (r), each looks like:

d(r) = d(0) + v(i)t + 0.5 a t^2

Since the d(r) values must differ by 0.1 km, in order for you to catch exactly up, you can subtract the equations appropriately. Then 0.1 km = 0.5 a t^2 . Ah, but that is 2 unknowns! So assume that you are at exactly 9 km, your competitor is at 9.1 km. The leader has run, let us assume, 9.1 km in 35 minutes. If the leader maintains his/her speed, you may determine t exactly (time to finish the race), and then proceed to find your required acceleration.

N.B. It would be unlikely in practice for you to win in this way! In general, your competitor probably will also be able to muster a final speed burst. And, it would be energetically more sensible to simply jump your own speed up immediately. That way, you will be closer to him/her in the final stretch. Just sayin'.