A particle travels first half of the total distance with constant speed `v_1` and second half with constant speed `v_2.` Find the average speed during the complete journey.

Options

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

Answer

C

Explanation

Time taken to travel first half distance `t_1 = (l//2)/(v_1) = (l)/(2 v_1)`
Time taken to travel second half distance `t_2 = (l)/(2 v_2)`
Total time `= t_1 + t_2`
=`(l)/(2 v_1) + (l)/(2 v_2) = (l)/(2) [(1)/(v_1) + (1)/(v_2)]`
We know that
`V_(av) = Average speed`
= total distance//total time
=`(l)/(1/2[(1)/(v_1) +(1)/(v_2)]] = (2 v_1 v_2)/((v_1 + v_2))`.