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 and the guard's room passes with velocity . The middle wagon of the train passes the pol

Question

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.

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(4)

Let 'S' be the distance between two ends $v$ be the constant acceleration

As we know $v^{2} - u^{2} = 2 a S$

Let $v_{c}$ be velocity at mid point.

Therefore,

$v_{c}^{2} - u^{2} = 2 a \frac{S}{2}$

$v_{c}^{2} = u^{2} + \frac{v^{2} - u^{2}}{2}$

$v_{c} = \sqrt{\frac{u^{2} + v^{2}}{2}}$

Solution

Q.
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.

1 $\frac{u + v}{2}$

2 $\frac{1}{2} \sqrt{u^{2} + v^{2}}$

3 $\sqrt{u v}$

4 $\sqrt{\frac{u^{2} + v^{2}}{2}}$

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Solution

Q. 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.

1 u+v2

2 12u2+v2

3 uv

4 u2+v22