Physics
Physics
1st Edition
Walker
ISBN: 9780133256925
Textbook solutions

All Solutions

Page 76: Practice Problems

Exercise 1
Step 1
1 of 3
In this problem, we compare the acceleration of three cars. We are given the following initial and final velocities and the time in which the car accelerates.
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}
Step 2
2 of 3
The acceleration is the rate of change of velocity. We have

$$
begin{align*}
a &= frac{Delta v}{t} \
a_{av, 1} &= frac{35~mathrm{m/s} – 25~mathrm{m/s}}{10~mathrm{s}} = 1.0~mathrm{m/s^{2}} \
a_{av, 2} &= frac{30~mathrm{m/s} – 0~mathrm{m/s}}{15~mathrm{s}} = 2.0~mathrm{m/s^{2}} \
a_{av, 3} &= frac{12~mathrm{m/s} – 32~mathrm{m/s}}{10~mathrm{s}} = -4.0~mathrm{m/s^{2}} \
end{align*}
$$

The rank in increasing order must be
$$
boxed{ a_{av, 3} < a_{av, 1} < a_{av, 2} }
$$

Result
3 of 3
$$
a_{av, 3} < a_{av, 1} < a_{av, 2}
$$
Exercise 2
Step 1
1 of 3
In this problem, we are winning that the winner of a race has velocity $v_text{f} = 140.3~mathrm{m/s}$. We find the winning time if it starts at rest and has an average acceleration of $a_text{av} = 30.4~mathrm{m/s^{2}}$.
Step 2
2 of 3
The velocity-acceleration equation must be

$$
begin{align*}
v_text{f} &= v_text{i} + a_text{av}t \
implies t &= frac{v_text{f} – v_text{i}}{a} \
&= frac{140.3~mathrm{m/s} – 0}{30.4~mathrm{m/s^{2}}} \
&= 4.61513~mathrm{s} \
t &= boxed{ 4.62~mathrm{s} }
end{align*}
$$

Result
3 of 3
$$
t = 4.62~mathrm{s}
$$
Exercise 3
Step 1
1 of 3
In this problem, the chameleon tongue accelerates to catch an insect. Its tongue accelerates with $a_text{av} = 33~mathrm{m/s^{2}}$ for time $t = 0.12~mathrm{s}$. We find the speed of the tongue as it reaches the insect.
Step 2
2 of 3
Begin, the tongue starts from rest, so the speed must be

$$
begin{align*}
v &= a_text{av}t \
&= left( 33~mathrm{m/s^{2}} right) left( 0.12~mathrm{s} right) \
&= 3.96~mathrm{m/s} \
v &= boxed{ 4.0~mathrm{m/s} }
end{align*}
$$

Result
3 of 3
$$
v = 4.0~mathrm{m/s}
$$
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