All Solutions
Page 76: Practice Problems
begin{center}
begin{tabular}{|l|c|c|c|}
hline
Car & $v_text{i}~(mathrm{m/s})$& $v_text{f}~(mathrm{m/s})$ & $t~(mathrm{s})$ \ hline
1 & 25 & 35 & 10 \ hline
2 & 0 & 30 & 15 \ hline
3 & 32 & 12 & 5 \ hline
end{tabular}
end{center}
$$
begin{align*}
a &= frac{Delta v}{t} \
a_{av, 1} &= frac{35~mathrm{m/s} – 25~mathrm{m/s}}{10~mathrm{s}} = 1.0~mathrm{m/s^{2}} \
a_{av, 2} &= frac{30~mathrm{m/s} – 0~mathrm{m/s}}{15~mathrm{s}} = 2.0~mathrm{m/s^{2}} \
a_{av, 3} &= frac{12~mathrm{m/s} – 32~mathrm{m/s}}{10~mathrm{s}} = -4.0~mathrm{m/s^{2}} \
end{align*}
$$
The rank in increasing order must be
$$
boxed{ a_{av, 3} < a_{av, 1} < a_{av, 2} }
$$
a_{av, 3} < a_{av, 1} < a_{av, 2}
$$
$$
begin{align*}
v_text{f} &= v_text{i} + a_text{av}t \
implies t &= frac{v_text{f} – v_text{i}}{a} \
&= frac{140.3~mathrm{m/s} – 0}{30.4~mathrm{m/s^{2}}} \
&= 4.61513~mathrm{s} \
t &= boxed{ 4.62~mathrm{s} }
end{align*}
$$
t = 4.62~mathrm{s}
$$
$$
begin{align*}
v &= a_text{av}t \
&= left( 33~mathrm{m/s^{2}} right) left( 0.12~mathrm{s} right) \
&= 3.96~mathrm{m/s} \
v &= boxed{ 4.0~mathrm{m/s} }
end{align*}
$$
v = 4.0~mathrm{m/s}
$$