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 <math> <mrow> <mi>u</mi> </mrow> </math> and the guard’s room passes with velocity <math> <mrow> <mi>v</mi> </mrow> </math> . The middle wagon of the train passes the pole with a velocity

Let S be the distance between Two ends a be the constant accelerationAs we know v 2 − u 2 = 2 a S or, a S = v 2 − u 2 2 Let v c be velocity at mid point.Therefore, v c 2 − u 2 = 2 a S 2  v c 2 = u 2 + a S  v c 2 = u 2 + v 2 − u 2 2  v c = u 2 + v 2 2

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 <math> <mrow> <mi>u</mi> </mrow> </math> and the guard’s room passes with velocity <math> <mrow> <mi>v</mi> </mrow> </math> . The middle wagon of the train passes the pole with a velocity

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Physics Class 11th Physics Motion in Straight Line

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

Option 1 -

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

Option 2 -

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

Option 3 -

$\sqrt[]{u v}$

Option 4 -

$\sqrt[]{(\frac{u^{2} + v^{2}}{2})}$

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1 Answer

Answered by

Raj Pandey | Contributor-Level 9

2 weeks ago

Correct Option - 4

Detailed 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, $a S = \frac{v^{2} - u^{2}}{2}$

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

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

$v_{c}^{2} = u^{2} + a S$

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

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

Let S be the distance between Two ends a be the constant accelerationAs we know <math> <mrow> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mi>a</mi> <mi>S</mi> </mrow> </math> or, <math> <mrow> <mi>a</mi> <mi>S</mi> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> Let <math> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mi>c</mi> </mrow> </msub> </mrow> </math>  be velocity at mid point.Therefore, <math> <mrow> <msubsup> <mrow> <mi>v</mi> </mrow> <mrow> <mi>c</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mi>a</mi> <mfrac> <mrow> <mi>S</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>  <math> <mrow> <msubsup> <mrow> <mi>v</mi> </mrow> <mrow> <mi>c</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>a</mi> <mi>S</mi> </mrow> </math>  <math> <mrow> <msubsup> <mrow> <mi>v</mi> </mrow> <mrow> <mi>c</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mfrac> <mrow> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>  <math> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mroot> <mrow> <mfrac> <mrow> <msup> <mrow> <mi>u</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math>

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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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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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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