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

Answer

D

Explanation

Let `l` be the length of the train
Ist case : `v^(2) - u^(2) = 2al`
II nd case: `v'^(2) - u^(2) = 2a (l//2)`
`rArr 2v'^(2) - 2u^(2) = 2al`
Comparing eqns, (i) and (ii),
`2v'^(2) - 2u^(2) = v^(2) - u^(2)`
`v' = sqrt((v^(2) + u^(2))/(2))`