Chapter 2, Problem 14E

A car travels on a straight, level road.

1. (a) Starting from rest, the car is going 44 ft/s (30 mi/h) at the end of 5.0 s. What is the car’s average acceleration in ft/s²?
2. (b) In 4.0 more seconds, the car is going 88 ft/s (60 mi/h). What is the car’s average acceleration for this time period?
3. (c) The car then slows to 66 ft/s (45 mi/h) in 3.0 s. What is the average acceleration for this time period?
4. (d) What is the overall average acceleration for the total time? (Note these convenient British unit conversions: 60 mi/h = 88 ft/s, 45 mi/h = 66 ft/s, and 30 mi/h = 44 ft/s.)

To determine

The average accleration of the car at the end of five seconds.

Answer to Problem 14E

The average accleration of the car at the end of five seconds is $8.8{\text{ ft/s}}^2$.

Explanation of Solution

Given info: The initial velocity of the car is zero, final velocity of the car is $44\text{ ft/s}$ and the time taken is $5\text{s}$.

Explanation:

The formula for the acceleration is as follows,

$a=\frac{v_f-v_o}{t}$

Here,

$a$ is the acceleration of the body

$v_f$ is the final velocity of the body

$v_o$ is the initial or original velocity of the body

$t$ is the time taken

Substitute $44\text{ ft/s}$ for $v_f$, $0\text{ ft/s}$ for $v_o$ and $5\text{s}$ for $t$.

$\begin{array}{c}a=\frac{44\text{ ft/s}-0\text{ ft/s}}{5\text{s}}\\ =8.8{\text{ ft/s}}^2\end{array}$

Conclusion:

Therefore, the average accleration of the car at the end of five seconds is $8.8{\text{ ft/s}}^2$.

To determine

The average accleration of the car at the another four seconds.

Answer to Problem 14E

The average accleration of the car at the another four seconds is ${\text{11 ft/s}}^2$.

Explanation of Solution

Given info: The final velocity of the car is $\text{88 ft/s}$ and the time taken is $4\text{s}$.

Explanation:

The final velocity at the end of $5\text{s}$ is the initial velocity for this case.

The formula for the acceleration is as follows,

$a=\frac{v_f-v_o}{t}$

Here,

$a$ is the acceleration of the body

$v_f$ is the final velocity of the body

$v_o$ is the initial or original velocity of the body

$t$ is the time taken

Substitute $44\text{ ft/s}$ for $v_o$, $\text{88 ft/s}$ for $v_f$ and $4\text{s}$ for $t$.

$\begin{array}{c}a=\frac{\text{88 ft/s}-44\text{ ft/s}}{4\text{s}}\\ =11{\text{ ft/s}}^2\end{array}$

Conclusion:

Therefore, the average accleration of the car at the another four seconds is ${\text{11 ft/s}}^2$.

To determine

The average accleration of the car at the another three seconds.

Answer to Problem 14E

The average accleration of the car at the another three seconds is $-7.33{\text{ ft/s}}^2$.

Explanation of Solution

Given info: The final velocity of the car is $\text{66 ft/s}$ and the time taken is $3\text{s}$.

Explanation:

The final velocity at the end of another four secondss is the initial velocity for this case.

The formula for the acceleration is as follows,

$a=\frac{v_f-v_o}{t}$

Here,

$a$ is the acceleration of the body

$v_f$ is the final velocity of the body

$v_o$ is the initial or original velocity of the body

$t$ is the time taken

Substitute $\text{88 ft/s}$ for $v_o$, $\text{66 ft/s}$ for $v_f$ and $3\text{s}$ for $t$.

$\begin{array}{c}a=\frac{\text{66 ft/s}-88\text{ ft/s}}{3\text{s}}\\ =-7.33{\text{ ft/s}}^2\end{array}$

Conclusion:

Therefore, the average accleration of the car at the another three seconds is $-7.33{\text{ ft/s}}^2$.

To determine

The overall average accleration of the car for the total time.

Answer to Problem 14E

The overall average accleration of the car for the total time is $5.5{\text{ ft/s}}^2$.

Explanation of Solution

Given info: The final velocity of the car is $\text{66 ft/s}$.

Explanation:

The final velocity of the car is $\text{66 ft/s}$, initial velocity of the car is $\text{0 ft/s}$.

The  total time $t$ taken is as follows,

$\begin{array}{c}t=\left(5\text{s + 4 s + 3s}\right)\\ =12\text{ s}\end{array}$

The formula for the acceleration is as follows,

$a=\frac{v_f-v_o}{t}$

Here,

$a$ is the acceleration of the body

$v_f$ is the final velocity of the body

$v_o$ is the initial or original velocity of the body

$t$ is the time taken

Substitute $\text{0 ft/s}$ for $v_o$, $\text{66 ft/s}$ for $v_f$ and $12\text{ s}$ for $t$.

$\begin{array}{c}a=\frac{\text{66 ft/s}-\text{0 ft/s}}{12\text{s}}\\ =5.5{\text{ ft/s}}^2\end{array}$

Conclusion:

Therefore, the overall average accleration of the car for the total time is $5.5{\text{ ft/s}}^2$.