Chapter 4, Problem 25P

To determine

Divide the example problem 8.3 in chapter 8 using the 4.2 section described in textbook into the format “Given” ,“Find” , and  “Solution”.

Answer to Problem 25P

The example problem 8.3 in chapter 8 is divided using the 4.2 section described in textbook into the format “Given” ,“Find” , and  “Solution”, and the total distance travelled by the car is $50347.2\text{m}$ and the average speed of the car over its entire distance is $99.2\frac{\text{km}}{\text{h}}$.

Explanation of Solution

Given:

Car accelerates at speed of $100\frac{\text{km}}{\text{h}}$ in 15 seconds from rest,

The car moves with constant speed of $100\frac{\text{km}}{\text{h}}$ for about 30 minutes,and

The car decelerates to a full stop in 10 seconds.

Find:

Find the total distance travelled by the car and also find its average speed over this distance.

Solution:

The car speed is linearly increased from zero to $100\frac{\text{km}}{\text{h}}$ for the first 15 seconds.

Therefore, the average speed of the car is $50\frac{\text{km}}{\text{h}}$ for this period.

Formula to determine the distance travelled during this period $\left(t_1\right)$ is,

$\begin{array}{c}{d}_1=\left(\text{time}\right)\left(\text{average}\text{speed}\right)\\ =\left(15\text{s}\right)\left(50\frac{\text{km}}{\text{h}}\right)\left(\frac{1\text{h}}{3600\text{s}}\right)\left(\frac{1000\text{m}}{1\text{km}}\right)\left[\begin{array}{l}\therefore 1\text{h}=3600\text{s,}\text{and}\\ \text{1}\text{km}\text{=1000}\text{m}\end{array}\right]\\ =208.3\text{m}\end{array}$

For the next 30 minutes (1800 s), the car travels with a constant speed of $100\frac{\text{km}}{\text{h}}$.

Formula to determine the distance travelled during this period $\left(t_2\right)$ is,

$\begin{array}{c}{d}_2=\left(\text{time}\right)\left(\text{average}\text{speed}\right)\\ =\left(1800\text{s}\right)\left(100\frac{\text{km}}{\text{h}}\right)\left(\frac{1\text{h}}{3600\text{s}}\right)\left(\frac{1000\text{m}}{1\text{km}}\right)\left[\begin{array}{l}\therefore 1\text{h}=3600\text{s,}\text{and}\\ \text{1}\text{km}\text{=1000}\text{m}\end{array}\right]\\ =50000\text{m}\end{array}$

For the last 10 sec, the car decelerates at a constant speed of $100\frac{\text{km}}{\text{h}}$ to zero and attains a full stop of the car.

Therefore, the average speed of the car during the last 10 sec is also $50\frac{\text{km}}{\text{h}}$ for this period

Formula to determine the distance travelled during this period $\left(t_3\right)$ is,

$\begin{array}{c}{d}_3=\left(\text{time}\right)\left(\text{average}\text{speed}\right)\\ =\left(10\text{s}\right)\left(50\frac{\text{km}}{\text{h}}\right)\left(\frac{1\text{h}}{3600\text{s}}\right)\left(\frac{1000\text{m}}{1\text{km}}\right)\left[\begin{array}{l}\therefore 1\text{h}=3600\text{s,}\text{and}\\ \text{1}\text{km}\text{=1000}\text{m}\end{array}\right]\\ =138.9\text{m}\end{array}$

Formula to determine the total distance covered by the car is,

$\begin{array}{c}d=d_1+d_2+d_3\\ =208.3\text{m}+50000\text{m}+138.9\text{m}\\ =50347.2\text{m}\end{array}$

Convert the unit of total distance from m to km

$\begin{array}{c}d=50347.2\text{m}\\ \text{=}\text{50}\text{.3472}\times {\text{10}}^3\text{m}\\ \text{=}\text{50}\text{.3472}\text{km}\end{array}$

Formula to determine the average speed of the car for the entire duration of the travel is,

$\begin{array}{c}{V}_{average}=\frac{\text{distance}\text{travelled}}{\text{time}}\\ =\frac{\text{50347}\text{.2}\text{m}}{1825\text{s}}\\ =27.58\frac{\text{m}}{\text{s}}\end{array}$

Convert the unit of average speed from $\frac{\text{m}}{\text{s}}$ to $\frac{\text{km}}{\text{h}}$.

$\begin{array}{c}{V}_{average}=\left(27.58\frac{\text{m}}{\text{s}}\right)\left(\frac{3600\text{s}}{1\text{h}}\right)\left(\frac{1\text{km}}{1000\text{m}}\right)\left[\begin{array}{l}\therefore 1\text{h}=3600\text{s,}\text{and}\\ \text{1}\text{km}\text{=1000}\text{m}\end{array}\right]\\ =99.2\frac{\text{km}}{\text{h}}\end{array}$

Conclusion:

Hence, the example problem 8.3 in chapter 8 is divided using the 4.2 section described in textbook into the format “Given” ,“Find” , and  “Solution”,