Question

A car moves from `X` to `Y` with a uniform speed `v_u` and returns to `Y` with a uniform speed `v_d`. The average speed for this round trip is :
A. `(2 v_d v_u)/(v_d + v_u)`
B. `sqrt(v_u v_d)`
C. `(v_d v_u)/(v_d + v_u)`
D. `(v_u + v_d)/(2)`

Answer 1

Correct Answer - A
We define
Average speed `= ("Distance travelled")/("Time taken") = (d)/(T)`
Let `t_1` and `t_2` be times taken by the car to go from `X` to `Y` and then from `Y` to `X` respectively.
Then, `t_1 + t_2 =[(XY)/(v_u)]+[(XY)/(v_d)] = XY((v_u + v_d)/(v_u v_d))`
Total distance travelled `d=XY+XY=2XY`
Therefore, average speed of the car for this round trip is.
`v_(av) = (2 XY)/(XY((v_u + v_d)/(v_u v_d)))` or `v_(av) = (2 v_uv_d)/(v_u + v_d)`.