The radius of the track.

Question

A racing car completes $5$ rounds of circle in $2$ mins . It has uniform centripetal acceleration $\pi^2 t^{-2}$ then the radius of circle is?. I asked it on physics $SE$ but I dont know how to ask questions there. So My try I let $\alpha=\pi^2$ so $a=\pi^2r$ also $a=\frac{v^2}{r}$ so $v=\pi.R$ also it covers $10\pi$ in $120$s . But don't know how to calculate the radius from it.

Answer 1

$\pi^2 t^{-2}$ need clarification as to what units these are in.

I am going to assume units are seconds and meters and so

Angular momementum = $\pi^2 m/sec^2 = v^2/r$

Length of lap = Circumference = $2 \pi r$.

$120sec*v = 5*(2\pi r)$ so $v = \frac{\pi}{12} r/sec$.

So $am = \pi^2 m/sec^2 = \frac{\pi^2}{144}r^2/sec^2*r= \frac{\pi^2}{144}r/sec^2$

So $r = \frac{144\pi^2 m*sec^2}{\pi^2*sec^2} = 144 m$.

That is if the units are meters and seconds, which was never specified.