Answer
a) The position after 2 hours is 146 miles.
b) $v(t)=65$
c) The car is going 67 mph at $t=3$. $s(3) = 202$ miles.
Work Step by Step
(a) The car's position after 2 hours is denoted by the expression $s(2)$. The position after 2 hours is
$$
s(2)=11(2)^2+2+100=44+2+100=146
$$
(b) The question is: "For what $t$ value is $v(t)=65$?
To find out when the car is going 67 mph , we set $v(t)=67$. We have
$$
\begin{aligned}
22 t+1 & =67 \\
22 t & =66 \\
t & =3 .
\end{aligned}
$$
The car is going 67 mph at $t=3$.
c) When $t=3, s(3)=11\left(3^2\right)+3+100=202$, so the car's position when it is going 67 mph is 202 miles.
