# Maths/Physics

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An athlete is training and is required to perform shuttle runs. From the starting position they sprint out to 10m (this takes 2 seconds). I know that a = 5m/s/s but I need to know at what metre within the run would maximum acceleration occur. Appreciate your help.
thanks

• Maths/Physics -

for all we know the acceleration is constant. I actually suspect the force is greatest when pushing off the starting block and therefore acceleration is greatest at the start (F = m a), but there is nothing in your statement to help us with a versus t. Therefore assume a is constant.
d = (1/2) a t^2
10 = (1/2) a (2^2)
20 = 4 a
a = 5 m/s^2 indeed

• Maths/Physics -

I think I know what you are looking for, so starting off where Damon left off:

Max acceleration occurs when the velocity=acceleration.

Vi=0m/s^2
Vf=5m/s and
a=5m/s^2
d=?

Solve for d.

(5m/s)^2=0+2(5m/s^2)d

25=10d
25/10=d

d=2.5m

The sprinters will not keep accelerating indefinitely, so I think this what your teacher/professor had in mind. But a better question would be when will the velocity equal the acceleration.

Best

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