Answer
By the Chain Rule
$a(t)$ = $\frac{dv}{dt}$ = $\frac{dv}{ds}{\frac{ds}{dt}}$ = $\frac{dv}{ds}v(t)$ = $v(t)\frac{dv}{ds}$
The derivative $\frac{dv}{dt}$ is the rate of change of the velocity
with respect to time (in other words, the acceleration) whereas the derivative $\frac{dv}{ds}$ is the rate of change of the velocity with
respect to the displacement.
Work Step by Step
By the Chain Rule
$a(t)$ = $\frac{dv}{dt}$ = $\frac{dv}{ds}{\frac{ds}{dt}}$ = $\frac{dv}{ds}v(t)$ = $v(t)\frac{dv}{ds}$
The derivative $\frac{dv}{dt}$ is the rate of change of the velocity
with respect to time (in other words, the acceleration) whereas the derivative $\frac{dv}{ds}$ is the rate of change of the velocity with
respect to the displacement.