# Question e9277

Aug 29, 2017

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,

$s = u t + \frac{1}{2} a {t}^{2}$

$200 = \frac{1}{2} a {19.19}^{2}$

$a \approx 1.1 m \cdot {s}^{- 2}$

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

$\int a \mathrm{dt} = \int \mathrm{dv}$

Oct 11, 2017

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

#### Explanation:

We can manipulate the suvat formula
$s = u \cdot t + \frac{1}{2} \cdot a {t}^{2}$
and arrive at $a = \frac{2 \left(s - u \cdot t\right)}{t} ^ 2$.
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.

$a = \frac{2 \left(200 m - 0 \cdot 19.19 s\right)}{19.19 s} ^ 2 = \frac{400 m}{368.25 {s}^{2}}$
$a = 1.086 \frac{m}{s} ^ 2$

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/CheetahSpeed_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