Kinematics

JEE Main level, single correct, medium

68 of 308

Question 68 of 308

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 uu and the guard's room passes with velocity vv. The middle wagon of the train passes the pole with a velocity.

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Answer: (D) (u2+v22)\sqrt{\left(\frac{u^2+v^2}{2}\right)}

Let ' SS ' be the distance between two ends ' aa ' be the constant acceleration As we know V2−u2=2aSV^2-u^2=2 a S
or, aS=V2−u22a S=\frac{V^2-u^2}{2}
Let VV be velocity at mid point.
Therefore, Vc2−u2=2aS2V_c^2-u^2=2 a \frac{S}{2}
Vc2=u2+aSVc2=u2+V2−u22Vc=u2+v22\begin{aligned} & V_c^2=u^2+a S \\ & V_c^2=u^2+\frac{V^2-u^2}{2} \\ & V_c=\sqrt{\frac{u^2+v^2}{2}} \end{aligned}

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