Question

A body covers a certain distance with a speed of 30km/h . It returns back with same distance with a speed of 50km/h. Then the average speed during the whole journey is

Answer 1

Given :

▪ A body covers a certain distance with a speed of 30kmph.

▪ It returns back with a speed of 50kmph.

To Find :

▪ Average speed during the whole journey.

Solution :

✒ Average speed is defined as the ratio of total distance travelled to the total time taken.

✒ Average speed is a scalar quantity.

✒ SI unit of average speed is m/s

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☞ Vav = (total distance travelled) ÷ (total time taken)

→ Vav = (d + d)/(t1 + t2)

• time = distance/velocity

→ Vav = 2d / (d/V1 + d/V2)

→ Vav = 2d(V1V2) / d(V1 + V2)

→ Vav = 2V1V2/(V1+V2)

→ Vav = 2×30×50/(30+50)

→ Vav = 3000/80

→ Vav = 37.5kmph

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✴ Short Trick :

▪ If body covers first half of the total distance at a speed of V1 and second half of the total distance at a speed of V2, then average speed of body is given by

$\bigstar\:\underline{\boxed{\bf{\purple{V_{av}=\dfrac{2V_1V_2}{V_1+V_2}}}}}\:\bigstar$

Answer 2

Given :-

$\sf\bullet Speed_1= 30km/h\\ \\ \sf\bullet Speed_2= 50km/h\\ \\ \sf\bullet\ \ Distance_1= Distance_2$

To find :-

The average speed of whole journey !

Now formula used

$\bigstar{\boxed{\sf{ Average \ speed= \dfrac{Total \ distance }{Total \ time}}}}$

• Let the distance be x
• Then find the T1

• We know that

$\implies\sf speed_= \dfrac{Distance }{Time } \\ \\ \implies\sf 30 = \dfrac{x}{T_1}\\ \\ \implies\sf T_1= \dfrac{x}{30}$

• Now Time when he return back
• Distance remains the same (x)

$\implies\sf 50 = \dfrac{x}{T_2}\\ \\ \implies\sf T_2= \dfrac{x}{50}$

• Now the average speed of body

$\longrightarrow\sf Av.\ speed = \dfrac{x+x}{\dfrac{x}{30}+\dfrac{x}{50}}\\ \\ \longrightarrow\sf Av.\ speed = \dfrac{2x}{\dfrac{5x+3x}{150}}\\ \\ \longrightarrow\sf Av.\ speed = \cancel{2x}\times \dfrac{150}{\cancel{8x}}\\ \\ \longrightarrow\sf Av.\ speed = \cancel{\dfrac{150}{4}}\\ \\ \longrightarrow{\red{\sf{ Average \ speed = 37.5km/h}}}$

$\underline{\textsf{\ Average \ speed \ of \ body ={\textbf{ 37.5km/h}}}}$