Question

A man went from his home to market 3 km away with a uniform speed of 4 km/h and on finding the market closed he instantly turns back with a velocity of 6 km/h. Find average speed of his journey

Answer 1

» To Find :

The Average speed of the man's journey .

» Given :

• Speed $\rightarrow v_{1} = 4 kmh^{-1}$

• Speed $\rightarrow v_{2} = 6 kmh^{-1}$

• Distance $\rightarrow s = 3 km$

» We Know :

Average speed :

$\sf{\underline{\boxed{Average\:Speed = \dfrac{s_{1} + s_{2}}{t_{1} + t_{2}}}}}$

Where ,

• s = Distance Covered
• t = time taken

Speed :

$\sf{\underline{\boxed{Speed = \dfrac{Distance\:Covered}{time\:taken}}}}$

» Concept :

To find the average speed ,first we have to find the time taken of the two journeys.

Here, the distance will be same in both the cases .i.e,

$s_{1} = s_{2} = 3 m$

From the formula of speed ,

$\sf{Speed = \dfrac{Distance\:Covered}{time\:taken}}$

We Get ,

$\sf{\underline{\boxed{time = \dfrac{Distance\:Covered}{Speed}}}}$

Substituting the values in it ,we get :

For First journey :

$\sf{\Rightarrow t_{1} = \dfrac{3}{4}}$

$\sf{\therefore t_{1} = \dfrac{3}{4} h}$

Hence, the time taken by the man in the first journey is $\dfrac{3}{4} h$

For Second Journey :

$\sf{\Rightarrow t_{2} = \dfrac{3}{6}}$

$\sf{\therefore t_{2} = \dfrac{\not{3}}{\not{6}} h}$

$\sf{\Rightarrow t_{2} = \dfrac{1}{2}}$

$\sf{\therefore t_{2} = \dfrac{1}{2} h}$

Hence, the time taken by the man in the first journey is $\dfrac{1}{2} h$

» Solution :

• Time taken $\rightarrow t_{1} = \dfrac{3}{4} h$

• Time taken$\rightarrow t_{2} = \dfrac{1}{2} h$

• Distance $\rightarrow s = 3 km$

Formula for Average speed :

$\sf{\underline{\boxed{Average\:Speed = \dfrac{s_{1} + s_{2}}{t_{1} + t_{2}}}}}$

Substituting the values in the formula ,and solving it ,we get :

$\sf{\Rightarrow Average\:Speed = \dfrac{3 + 3}{\dfrac{3}{4} + \dfrac{1}{2}}}$

$\sf{\Rightarrow Average\:Speed = \dfrac{6}{\dfrac{3 + 2}{4}}}$

$\sf{\Rightarrow Average\:Speed = \dfrac{6}{\dfrac{5}{4}}}$

$\sf{\Rightarrow Average\:Speed = \dfrac{6}{5} \times 4}$

$\sf{\Rightarrow Average\:Speed = \dfrac{24}{5}}$

$\sf{\Rightarrow Average\:Speed = 4.8 kmh^{-1}}$

Hence, the average speed of the man is 4.8 km/h.

Additional information :

• First Equation of motion = v = u + at

• Second Equation of motion = s = ut + ½at²

• Third Equation of motion = v² = u² + 2as