Question

A body covers half of it's journey with speed 'a' m/s and the other half with the speed 'b' m/s. Calculate the average speed of the body during the whole journey.

Answer 1

This is your answer

Answer 2

Answer:

Explanation:

Solution :-

Suppose the total distance covered by the body is (2d), out of which (d) is covered with a speed (a) and the other half (i.e, d) is covered with a speed (b).

Let us suppose (t₁) and (t₂) be the time taken for the first and second half respectively.

t₁ = d/a and t₂ = d/b

Total time taken, t = t₁ + t₂

$\sf=\dfrac{d}{a}+\dfrac{d}{b}={\bf d(\dfrac{1}{a}+\dfrac{1}{b})}$

Also, t₁ + t₂ = 2d/v(avg)

Therefore,

$\sf\implies \dfrac{2d}{v(avg)}=d(\dfrac{1}{a}+\dfrac{1}{b})$

$\sf\implies \dfrac{2d}{v(avg)}=(\dfrac{a+b}{ab})$

$\bf\implies \dfrac{2d}{v(avg)}=(\dfrac{2ab}{a+b})$

Hence, the average speed of the body during the whole journey is $\bf(\dfrac{2ab}{a+b})$.