If a car covers 2/5th of the total distance with v1 speed and 3/5 th distance with v2 then the average speed is

Q: If a car covers 2/5th of the total distance with v1 speed and 3/5 th distance with v2 then the average speed is

(a) $\large \frac{1}{2}\sqrt{v_1 v_2} $

(b) $\large \frac{v_1 + v_2}{2}$

(c) $\large \frac{2 v_1 v_2 }{v_1 + v_2}$

(d) $\large \frac{5 v_1 v_2 }{3 v_1 + 2 v_2}$

Ans: (d)

Sol: Average Speed $\large v_{avg} = \frac{s_1 + s_2}{s_1/v_1 + s_2/v_2}$

$\Large = \frac{\frac{2 s}{5}+ \frac{3s}{5}}{\frac{2s}{5v_1}+ \frac{3s}{5v_2}}$

$\large = \frac{2+3}{\frac{2}{v_1} + \frac{3}{v_2}}$

$\large = \frac{5 v_1 v_2 }{3 v_1 + 2 v_2}$