Answer
a) Until the speed reaches $45 \mathrm{mi} / \mathrm{h}$, Car takes 2 seconds
b) Before stopping, Car travels $352 \mathrm{ft}$
Work Step by Step
$(a)$
\[
\begin{array}{c}
v=60 \mathrm{mi} / \mathrm{h}=88 \mathrm{ft} / \mathrm{s} \\
\qquad -11=a(t) \\
\therefore v(t)=\int a(t) d t=-11 \int d t=11 t+C \\
\because v(0)=88 \Rightarrow C=88 \\
v(t)=88-11 t
\end{array}
\]
When $v(t)=45 \mathrm{mi} / \mathrm{h}=66 \mathrm{ft} / \mathrm{s}$
\[
\therefore 66=88-11 t \Rightarrow 2 s=t
\]
And therefore, for the speed to reach $45 \mathrm{mi} / \mathrm{h}$, Car takes 2 seconds
$(b)$
\[
x(t)=\int(88-11 t) d t=88 t-\frac{11 t^{2}}{2}+C
\]
When $t=0 \Rightarrow x(0)=0 \Rightarrow C=0$
$\therefore x(t)=-\frac{11 t^{2}}{2}+88 t$
When the car stops $v(t)=0 \Rightarrow 0=88-11 t \Rightarrow 8 s=t$
\[
x(t)=88(8)-\frac{11(8)^{2}}{2}=352
\]
And therefore, before stopping, the car travels $352 \mathrm{ft}$
