In a relay race, a sprinter receives the baton 100m from the finish when his speed is 8.8m/s. He then accelerates uniformly for 2s until he reaches his top speed, which he maintains for the remainder of the race. His time for the 100m is recorded as 10.6s.

Calculate the sprinter's top speed.

I've set up a velocity/time graph like in the attached image.

I know the UVATS equations but I can only identify two terms with which to find v.

v = u + at

v^2 - u^2 = 2as

s = ut + (at^2)/2

s = t(u + v)/2

u = 8.8m/s

v = ?

a = ?

t = 2s

s = ?

I think I have to somehow determine the displacement in section B to find the displacement in section A. I can see that the final velocity must be determinable because the acceleration happens over 2 seconds and 8.6 seconds remain, and that if he accelerated to some high velocity he would have finished the 100m sooner, but I can't figure out the solution.

Thanks in advance.

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This post has been edited by **Coding in the name of**: 06 December 2012 - 12:16 PM