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 + v)/(2)`
B. `(1)/(2) sqrt(u^(2) + v^(2))`
C. `sqrtuv`
D. `sqrt(((u^(2) + v^(2))/(2)))`

Answer

D

Explanation

Let the length of train is s, then by third equation of motion `v^(2) = u^(2) + 2a xx s` …(1)
Where v is final velocity after travelling a distance s with an acceleration a & u is initial velocity as per question
Let velocity of middle point of train at same point is v.. then `(v.)^(2) = u^(2) + 2a xx (s//2)` ..(2)
By equations (1) and (2), we get `v.= sqrt((v^(2) + u^(2))/(2))`