Answer
$$
v(t)=s^{\prime}(t)=2t - \sin t , \quad s(0)=3
$$
The position of the particle is
$$
s(t)=t^{2} + \cos t+2.
$$
Work Step by Step
$$
v(t)=s^{\prime}(t)=2t - \sin t , \quad s(0)=3
$$
The general anti-derivative of $
s^{\prime}(t)=2t - \sin t
$ is
$$
s(t)=t^{2} + \cos t+C
$$
To determine C we use the fact that $s(0)=3$:
$$
s(0)=(0)^{2} + \cos (0)+C =3
$$
$ \Rightarrow $
$$
1+C=3 \quad \Rightarrow \quad C=2,
$$
so the position of the particle is
$$
s(t)=t^{2} + \cos t+2.
$$
