A car racer was initially at rest. He accelerated uniformly at 11m/s/s for a distance of 200m. How long did it take the car to cover this distance?

Question

I was trying to find its final velocity but it was incorrect since I need the final velocity so that I can solve the time on how long did it take for the car to cover the distance.

Answer 1

Hint: Use the formula $$\frac{at^2}{2}=S \iff t=\sqrt{\frac{2S}{a}}$$

Answer 2

You can model the exact velocity-time graph as $v=11t$. This is because the gradient of this line gives the acceleration or rate of change of velocity, which is $11$.

So the integral equation you'd be solving is:

$\displaystyle \int_0^t 11x \mathrm dx=200$

$\left[\dfrac{11}{2}x^2\right]_0^t=200$

$\dfrac{11}{2}t^2=200$

Of course there's a formula, but it didn't come out of nowhere.