Answer
Please see the work below.
Work Step by Step
We know that
$a_r=\frac{v^2}{r}$
Differentiating both sides w.r.t 't' , we obtain:
$\frac{da_r}{dt}=\frac{d}{dt}(\frac{v^2}{r})$
$\implies \frac{da_r}{dt}=\frac{r\frac{dv^2}{dt}-v^2\frac{dr}{dt}}{r^2} $
$\implies \frac{da_r}{dt}=\frac{2vr\frac{dv^2}{dt}-v^2\frac{dr}{dt}}{r^2}$
$\implies \frac{da_r}{dt}=\frac{2vrat-v^2\frac{dr}{dt}}{r^2}$
$\implies \frac{da_r}{dt}=\frac{2vat}{r}-\frac{v^2}{r^2}\frac{dr}{dt}$
