Question

Question #e9277

Answer 1

There is.

Explanation:

Now of course usain bolt will start the sprint from rest as we have practically seen.Thus, we can take the initial velocity as zero.

Assuming acceleration constant,

`s=ut+1/2at^2`

`200=1/2a19.19^2`

`a~~1.1m*s^(-2)`

But if the acceleration isn't constant the information is insufficient as in that case, we have to integrate acceleration using the following formula:

`intadt=intdv`

Answer 2

Usain Bolt's average acceleration is 1.086 m/s^2.

Explanation:

We can manipulate the suvat formula
`s = u*t + 1/2*at^2`
and arrive at `a = (2(s - u*t)) / t^2`.
If we plug in our data, that will provide a value of acceleration that would take an object 200 m in 19.19 s.
So I will do that.

`a = (2(200 m - 0*19.19 s)) / (19.19 s)^2 = (400 m)/(368.25 s^2)`
`a = 1.086 m/s^2`

So that is Usain Bolt's average acceleration. That value of acceleration, would take an object 200 m in 19.19 s if used for the entire 200 m.

Usain Bolt could not use that strategy for that race. His speed would be up to only 3 m/s after 3 second of running while everyone else would be at their full speed. Usain could not actually maintain that value of acceleration in a 200 m because after 19 s that would have him running at about 19 m/s - or about 68 Kilometers per Hour. That is slightly faster than a cheetah in a chase.
Ref: https://en.wikipedia.org/wiki/Cheetah#Speed_and_acceleration

So Usain Bolt - and all sprinters - uses maximum acceleration at the start to get up to full speed quickly and continue at a good pace throughout.

I hope this helps,
Steve