Question

Two cyclists are in a race. One cyclist knows that he is slower, so he cheats: he removes the faster cyclist’s bike chain. The cheater starts from rest immediately with acceleration 2.1 m/s2. The faster cyclist has to take 4 seconds to replace her bike chain. She then follows (also from rest) with acceleration 2.9 m/s2. Assume that both cyclists accelerate smoothly and that they do not reach their maximum speeds during this race.

What is the maximum length that the race can be (in meters) in order for the slower cyclist to win?

Answer 1

Mathematically, the problem is to find the distance from the starting point where the faster cyclist will be able to overtake the slower one. Because if the track length is shorter than that distance, the faster person will never be able to overtake the slower one as the race will end before that!

The method is to find the time in which the distance travelled by slow (s1) will be equal to distance travelled by fast (s2).

Using s=ut+1/2at\(^{2}\)
Now u=0.

For slower cyclist :-

s1=1/2a\(_{1}\)t\(^{2}\) where a\(_{1}\)=2.1m/s\(^{2}\)

Similarly for faster person :-

s2=1/2a\(_{2}\)(t-4)\(^{2}\) where a\(_{2}\)=2.9m/s\(^{2}\)

Why did i use (t-4) is at the heart of this question. The faster cyclist only had (t-4) seconds to travel while the faster one had complete 't' seconds.

Now put s1=s2 and solve for t. Then put t in either of these 2 eqns and find s1(or s2 ,which are equal) .