91Ó°ÊÓ

• Distance D$=\mathbf{12}\mathbf{km}$.
• Time = $\mathbf{18}\mathbf{\text{ }}\mathbf{min}\mathbf{=}\mathbf{\text{18/60 h}}\mathbf{=}\mathbf{\text{0.3 h´Ç³Ü°ù}}$

a)

The average speed of the girl is the ratio of the distance covered to that of the time period.

In this case, the formula is :

$\mathbf{\text{´¡±¹±ð°ù²¹²µ±ð S±è±ð±ð»å}}\mathbf{=}\frac{\mathbf{\text{Distance}}}{\mathbf{\text{Time}}}$

Substituting the values in the above expression, we get:

$\begin{array}{c}\mathrm{s}=\frac{12\text{ k³¾}}{0.3\text{ h}}\\ =40\text{ k³¾/³ó}\end{array}$

Hence the average speed when she goes to school is $\mathbf{40}\mathbf{km}\mathbf{/}\mathbf{hr}$.

b)

The displacement to that of the time taken to cover that displacement is called the time period.

The displacement is the shortest length between the initial and final positions.

The shortest distance from her school to her house is given in the question as $\mathbf{10}.\mathbf{3}\mathbf{km}$.

Hence the displacement of the girl will be $\mathbf{10}.\mathbf{3}\mathbf{km}$.

$\mathrm{Average}\text{ }\mathrm{Velocity}=\frac{\mathrm{Displacement}}{\mathrm{Time}}$

Substituting the values in the above expression, we get:

$\begin{array}{c}\mathrm{v}=\frac{10.3\text{ k³¾}}{0.3\text{ h}}\\ =34.33\text{ k³¾/³ó}\end{array}$

The average velocity of the girl will be $\mathbf{34}.\mathbf{33}\text{k}\mathbf{m}/\mathbf{h}$.

c)

The total time is taken to cover the distance is$\mathbf{7}\text{ }\mathbf{h}\text{ }\mathbf{30}\text{ }\mathbf{min}$.

Hence it will be$\mathbf{7}.\mathbf{5}\text{ }\mathbf{h}$.

The girl is traveling a total of$\mathbf{12}\mathbf{km}$from home to school and coming back$\mathbf{12}\mathbf{km}$from school to home.

Hence the total distance traveled $=12\text{ k³¾}+12\text{ k³¾}=24\text{ k³¾}$.

Average speed can be calculated as:

$\mathbf{Average}\mathbf{\text{ }}\mathbf{Speed}\mathbf{=}\frac{\mathbf{Distance}}{\mathbf{Time}}$

Substituting the values in the above expression, we get:

$\begin{array}{c}\mathrm{s}=\frac{24\text{ k³¾}}{7.5\text{ h}}\\ =3.2\text{ k³¾/³ó}\end{array}$

Hencethe speed of the girl going to school and then returning is $\mathbf{3}\mathbf{.}\mathbf{2}\mathbf{\text{ k³¾/³ó}}$.

Here as the initial and the final position of the girl is her house, the minimum or shortest distance between the initial and final position will be zero.

Hence the displacement will be zero.

Therefore, the average velocity of the body will be zero