Engine of a train that is moving with unifrom acceleration passes a pole with speed `u` while the last compartment passes the pole with speed 'v'. The middle point of the train passes the given pole with speed:

Options

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

Answer

D

Explanation

`vec(v)^(2)=u^(2)+2al`.
`rArr 2al. =v^(2)-u^(2)`
also `v_(m)^(2)=u^(2)+2a(L)/(2)=u^(2)+(1)/(2)(v^(2)-u^(2))`
`=(2u^(2)+v^(2)-u^(2))/(2)=(u^(2)+v^(2))/(2)`
`v_(m)=sqrt((u^(2)+v^(2))/(2))`