Answer
$$
s(t)=10+\frac{1}{4} \sin (10 \pi t)
$$
$\Rightarrow$
the velocity after $ t$ seconds is
$$ v(t)=s^{\prime}(t)=\frac{1}{4} \cos (10 \pi t)(10 \pi)=\frac{5 \pi}{2} \cos (10 \pi t) \mathrm{cm} / \mathrm{s}
$$
So, the velocity of the particle after $t$ seconds is $\frac{5 \pi}{2} \cos (10 \pi t) \mathrm{cm} / \mathrm{s}$.
Work Step by Step
$$
s(t)=10+\frac{1}{4} \sin (10 \pi t)
$$
$\Rightarrow$
the velocity after $ t$ seconds is
$$ v(t)=s^{\prime}(t)=\frac{1}{4} \cos (10 \pi t)(10 \pi)=\frac{5 \pi}{2} \cos (10 \pi t) \mathrm{cm} / \mathrm{s}
$$
So, the velocity of the particle after $t$ seconds is $\frac{5 \pi}{2} \cos (10 \pi t) \mathrm{cm} / \mathrm{s}$.
