The two ends of a train moving with a constant acceleration pass a certain point with velocities M and w. The velocity with which the middle point of a train passes the same point is:

Options

A. `(u+v)/(2)`
B. `(u^(2)+v^(2))/(2)`
C. `sqrt((u^(2)+v^(2))/(2))`
D. `sqrt((u^(2)+v^(2))`

Answer

c

Explanation

If l be the length of train and `a` be the acceleration then `v^(2)-u^(2)=2al`
Also if `v_(1)` is speed of middle points of trains,
then `v_(1)^(2)-u^(2)=2a(l)/(2)`
or `v_(1)^(2)-u^(2)=(v_2 -u_2)/(2)`
`2v_(1)^(2)-2u^(2)=v^(2)-u^(2)`
`v_(1)^(2)=(v^(2)+u^(2))/(2)` `:. v_1 sqrt((v^(2)+u^(2))/(2))`