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JEE Main2012PhysicsMotion in One DimensionActual

A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity u and the guard's room passes with velocity v . The middle wagon of the train passes the pole with a velocity.

Options

  1. Au+v 2
  2. B1 2 u^2+v^2
  3. Cu v
  4. D( u^2+v^2 2 )

Correct answer

D. ( u^2+v^2 2 )

Step-by-step solution

Let ' S ' be the distance between two ends ' a ' be the constant acceleration As we know V^2-u^2=2 a S or, a S= V^2-u^2 2 Let V be velocity at mid point. Therefore, V_c^2-u^2=2 a S 2 aligned & V_c^2=u^2+a S & V_c^2=u^2+ V^2-u^2 2 & V_c= u^2+v^2 2 aligned

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