Answer
a) $v(t)=-Aw\sin(wt+\delta)$
b) $t=\frac{k\pi-\delta }{w}$ where $k \in \mathbb Z$.
Work Step by Step
$a)$
$$v(t)=s'(t)=-A(wt+\delta)'\sin(wt+\delta)$$
$$v(t)=s'(t)=-Aw\sin(wt+\delta)$$
$b)$
$$-Aw\sin(wt+\delta)=0 \to \sin(wt+\delta)=0 \to wt+\delta=k\pi \to t=\frac{k\pi-\delta }{w}$$ where $k \in \mathbb Z$.
