Answer
(b) $2.1 \mathrm{s}$
(c) $5.5 \mathrm{s}$
(a) $-24.2 \mathrm{ft} / \mathrm{s}^{2}$
Work Step by Step
(a)
We find:
$88=v(t)=132+a t \Rightarrow -\frac{44}{a}=t$
$200=s(t)=-\frac{3872}{a}+\frac{1936 a}{2 a^{2}}=\frac{-4840}{a}$
$a=-24.2$
$s(t)=200, v_{0}=90$ $\mathrm{mi} / \mathrm{h}=132 \mathrm{ft} / \mathrm{s}, s_{0}=0$, $v(t)=60 \mathrm{mi} / \mathrm{h}=88$
$\mathrm{ft} / \mathrm{s}$
(b) Using the velocity function:
$v(t)=132-24.2 t=80 \frac{2}{3}$
$\Rightarrow t=\frac{51 \frac{1}{3}}{-24.2} \approx 2.1$
Using (11) with $v(t)=55 \mathrm{mi} / \mathrm{h}$ $=80 \frac{2}{3} \mathrm{ft} / \mathrm{s}$ and $a=-24.2$, $v_{0}=132$
(c) $0=v(t)=132-24.2 t$
$\Rightarrow t=\frac{-132}{-24.2} \approx 5.5$
Using formula (11) with $v(t)=0$ and $v_{0}=132$: $a=$ -24.2
