For `(1)/(m)` of the distance between two stations a train is uniformly accelerated and `(1)/(n)` of the distance it is uniformly retarded. It starts from rest at one station and comes to rest at the other. The ratio of the greatest velocity to the average velocity will be:

Options

A. `(1 + (1)/(m) - (1)/(n))`
B. `(1 + (1)/(m) + (1)/(n))`
C. `((1)/(m) + (1)/(n) - 1)`
D. `((1)/(m) + (1)/(n))`

Answer

B

Explanation

`2a_(1) xx (s)/(m) = (v_("max"))^(2)`
Also `(v_("max"))^(2) = 2a_(2) xx (s)/(n)`
Av. velocity `= (s)/(t_(1) + t_(2))` Where `t_(1) = (v_("max"))/(a_(1))`
and `t_(2) ((v_("max"))/(a_(2)))`