A vehicle travels half the distance (L) with speed ` V_1` and the other half with speed ` V_2`, then its average speed is .

Options

A. `(v_1+v_2)/(2)`
B. `(2v_1 +v_2)/(v_1+v_2)`
C. `(2v_1v_2)/(v_1+v_2)`
D. `((v_1v_2))/(v_1+v_2)`

Answer

C

Explanation

Time taken to travel first half distance,
`t_1 = (L//2)/(v_1) = (L)/(2v_1)`
Time taken to travel second half distance, `t_2 = (L // 2)/(v_2) = (L)/(2v_2)` Total time taken =`t_1 +t_2 = (L)/(2v_1) +(L)/(2v_2) `
` v_(av) = (L)/( (L)/(2v_1) + (L)/(2v_2) ) = (1)/(1/2 [ (1)/(v_1) +(1)/(v_2) ] ) = (2v_1v_2)/(v_2 +v_1)`