Answer
$$
a(t)=5t^{2}+4,\quad \quad [V(0)=6]
$$
The velocity is given by:
$$
V(t) =\frac{5t^{3}}{3}+4t+6.
$$
Work Step by Step
$$
a(t)=5t^{2}+4,\quad \quad [V(0)=6]
$$
To find the velocity $V(t)$ by integrating the acceleration $a(t)$ as follows:
$$
\begin{aligned}
V(t) &=\int (5t^{2}+4) dt \\
&=\frac{5t^{3}}{3}+4t+C
\end{aligned}
$$
for some constant $C$. Find $C$ from the given information that $V(t)=6$ when $t=0.$
$$
\begin{aligned}
V(0) =\frac{5(0)^{3}}{3}+4(0)+C&=6\\
C&=6
\end{aligned}
$$
So,
$$
V(t) =\frac{5t^{3}}{3}+4t+6
$$
