Chapter 1, Problem 31P

(a)

To determine

To Convert: The given value in $\text{km}/\left(\text{h}\cdot \text{s}\right)$ .

Answer to Problem 31P

  $36\text{km}/\left(\text{h}\cdot \text{s}\right)$

Explanation of Solution

Given:

The value of acceleration is $1.296\times {10}^5\text{km}/{\text{h}}^2$ .

Formula used:

Change in velocity within unit time is defined as acceleration.

Write the expression for acceleration.

  $a=\frac{\Delta v}{\Delta t}$

Here, $\Delta v$ is the change in velocity, $\Delta t$ is time interval and $a$ is acceleration of object.

SI unit of acceleration is $\text{m}/{\text{s}}^2$ ; other unit of acceleration is $\text{km}/{\text{h}}^2$ ; $1\text{hr}$ is equal to $3600\text{s}$ .

Calculation:

Convert acceleration from $\text{km}/{\text{h}}^2$ to $\text{km}/\left(\text{h}\cdot \text{s}\right)$ .

  $\begin{array}{c}a=\left(1.296\times {10}^5\text{km}/{\text{h}}^2\right)\left(\frac{1\text{km}/\left(\text{h}\cdot \text{s}\right)}{3600\text{km}/{\text{h}}^2}\right)\\ =36\text{km}/\left(\text{h}\cdot \text{s}\right)\end{array}$

Conclusion:

Thus, the value of acceleration is equal to $36\text{km}/\left(\text{h}\cdot \text{s}\right)$ .

(b)

To determine

To Convert: The given value in $\text{m}/{\text{s}}^2$ .

Answer to Problem 31P

  $10\text{m}/{\text{s}}^2$

Explanation of Solution

Given:

The value of acceleration is $1.296\times {10}^5\text{km}/{\text{h}}^2$ .

Formula used:

Change in velocity within unit time is defined as acceleration.

Write the expression for acceleration.

  $a=\frac{\Delta v}{\Delta t}$

Here, $\Delta v$ is the change in velocity, $\Delta t$ is time interval and $a$ is acceleration of object.

SI unit of acceleration is $\text{m}/{\text{s}}^2$ ; other unit of acceleration is $\text{km}/{\text{h}}^2$ ; $1\text{hr}$ is equal to $3600\text{s}$ ; $1\text{km}$ is equal to $1000\text{m}$ .

Calculation:

Convert acceleration from $\text{km}/{\text{h}}^2$ to $\text{m}/{\text{s}}^2$ .

  $\begin{array}{c}a=\left(1.296\times {10}^5\text{km}/{\text{h}}^2\right)\left(\frac{1000\text{ m}}{1\text{km}}\right)\left(\frac{1\text{h}}{\text{3600 s}}\right)\left(\frac{1\text{h}}{\text{3600 s}}\right)\\ =10{\text{ m/s}}^2\end{array}$

Conclusion:

Thus, the value of acceleration is equal to $10{\text{ m/s}}^2$ .

(c)

To determine

To Convert: The given value in $\text{ft}/\text{s}$ .

Answer to Problem 31P

  $88\text{ft}/\text{s}$

Explanation of Solution

Given:

The value of velocity is $60\text{mi}/\text{h}$ .

Formula used:

Velocity is defined as total displacement covered within unit time.

Write the expression for velocity.

  $v=\frac{s}{t}$

Here, $s$ is the displacement, $t$ is time interval and $v$ is velocity of object.

SI unit of velocity is $\text{m}/\text{s}$ ; other unit of velocity is

  $\text{mi}/\text{h}$ and $\text{ft}/\text{s}$ ; $1\text{hr}$ is equal to $3600\text{s}$ ; $1\text{mi}$ is equal to $5280\text{ft}$ .

Calculation:

Convert velocity from $\text{mi}/\text{h}$ to $\text{ft}/\text{s}$ .

  $\begin{array}{c}v=\left(60\text{mi}/\text{h}\right)\left(\frac{5280\text{ft}}{1\text{ mi}}\right)\left(\frac{1\text{ h}}{3600\text{ s}}\right)\\ =88\text{ft}/\text{s}\end{array}$

Conclusion:

Thus, the value of velocity is equal to $88\text{ft}/\text{s}$ .

(d)

To determine

To Convert: The given value in $\text{m}/\text{s}$ .

Answer to Problem 31P

  $26.8\text{m}/\text{s}$ .

Explanation of Solution

Given:

The value of velocity is $60\text{mi}/\text{h}$ .

Formula used:

Velocity is defined as total displacement covered within unit time.

Write the expression for velocity.

  $v=\frac{s}{t}$

Here, $s$ is the displacement, $t$ is time interval and $v$ is velocity of object.

SI unit of velocity is $\text{m}/\text{s}$ ; other unit of velocity is $\text{mi}/\text{h}$ and $\text{ft}/\text{s}$ ; $1\text{hr}$ is equal to $3600\text{s}$ ; $1\text{mi}$ is equal to $1609\text{m}$ .

Calculation:

Convert velocity from $\text{mi}/\text{h}$ to $\text{ft}/\text{s}$ .

  $\begin{array}{c}v=\left(60\text{mi}/\text{h}\right)\left(\frac{1609\text{ft}}{1\text{ mi}}\right)\left(\frac{1\text{ h}}{3600\text{ s}}\right)\\ =26.8\text{m}/\text{s}\end{array}$

Conclusion:

Thus, the value of velocity is equal to $26.8\text{m}/\text{s}$ .