Answer
See explanation.
Work Step by Step
Acceleration is constant
\[
a=a(t)
\]
Velocity is an integral part of the acceleration
\[
\begin{array}{l}
v(t)=\int a(t) d t=\int a d t=a t+C \\
v(0)=v_{0}=C
\end{array}
\]
So $v_{0}+a t=v(t)$
The position is the integral of the velocity
\[
\begin{array}{l}
s(t)=\int v(t) d t=v_{0} t+\frac{a}{2} t^{2}+C \\
s(0)=s_{0}=C
\end{array}
\]
So $s(t)=s_{0}+v_{0} t+\frac{a}{2} t^{2}$
