Question

The two ends of a train moving with constant acceleration pass a certain point with velocities u and v. The velocity with which the middle point of the train passes the same point is
(a) (u + v)/{2}(b) ${(u^{2} + v^{2})}/{2}$(c) $\sqrt{\frac{(u^{2} + vu^{2})}{2}}$(d) $\sqrt{u^{2} + v^{2}}$

Answer 1

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Answer 2

Let the length of train be L

As it crosses the point the initial velocity will be u and final velocity be v

Thus,

v²-u²=2aL or v²=u²+2aL (1 eq)

a=v²-u²/2L

For finding the mid-point of the train , the distance travelled will be -

L1=L/2

= v² = u²+2a(L/2)

= v² = u²+1/2×(v²-u²) by equation 1

= v² = ( v²+u²)/2

= v = [v²+u² /2] to the power 1/2