Answer
$(a) \frac{ds}{dt} = \frac{1}{2} s$
$(b) \frac{d^2s}{dt^2} = 2 \frac{ds}{dt}$
Work Step by Step
$(a)$ To find the velocity, differentiate $s$ one time. Since the displacement
$s(t)$ is always half,
$ \frac{ds}{dt} = \frac{1}{2} s$
$(b)$ To find the acceleration, differentiate $s$ for the second time. Since the acceleration is always twice the velocity, $\frac{ds}{dt}$:
$\frac{d^2s}{dt^2} = 2 \frac{ds}{dt}$
