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Question

The two ends of a train moving with uniform 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
v2+u22
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B
v+u2
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C
v+u
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D
v2+u22
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Solution

Since the train has uniform acceleration, we know,

v2=u2+2 al ( l=length of train ),
so the acceleration of the train can be found out using this, so, a =v2u22l.

For the central point to find the velocity:

s or the displacement will be half the length of the train that is 'l' at the midpoint and velocity at the midpoint will be vm.
So, v2m=u2+2al2v2mu2=al
v2mu2=v2u22v2m=v2+u22
vm=v2+u22

Physics

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