An engine of a train, moving with uniform acceleration, passes the signal – post with velocity u and the last compartment with velocity <math> <mrow> <mi>υ</mi> <mo>.</mo> </mrow> </math> The velocity with which middle point of the train passes the signal post is:

Assume the length of train be I and its acceleration be a. v 2 = u 2 + 2 a l ⇒ a l = v 2 − u 2 2 Velocity when middle point crosses the post, V m = u 2 + 2 a l 2 . = u 2 + v 2 − u 2 2 = u 2 + v 2 2

An engine of a train, moving with uniform acceleration, passes the signal – post with velocity u and the last compartment with velocity <math> <mrow> <mi>υ</mi> <mo>.</mo> </mrow> </math> &nbsp;The velocity with which middle point of the train passes the signal post is:

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Physics Class 11th Physics Motion in Straight Line

An engine of a train, moving with uniform acceleration, passes the signal – post with velocity u and the last compartment with velocity $υ .$ The velocity with which middle point of the train passes the signal post is:

Option 1 -

$\frac{u + υ}{2}$

Option 2 -

$\sqrt[]{\frac{υ^{2} + u^{2}}{2}}$

Option 3 -

$\frac{υ - u}{2}$

Option 4 -

$\sqrt[]{\frac{υ^{2} - u^{2}}{2}}$

2 Views | Posted 2 weeks ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 weeks ago

Correct Option - 2

Detailed Solution:

Assume the length of train be I and its acceleration be a.

$v^{2} = u^{2} + 2 a l \Rightarrow a l = \frac{v^{2} - u^{2}}{2}$

Velocity when middle point crosses the post,

$V_{m} = \sqrt[]{u^{2} + 2 a \frac{l}{2}} . = \sqrt[]{u^{2} + \frac{v^{2} - u^{2}}{2}} = \sqrt[]{\frac{u^{2} + v^{2}}{2}}$

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An engine of a train, moving with uniform acceleration, passes the signal – post with velocity u and the last compartment with velocity $υ .$ The velocity with which middle point of the train passes the signal post is:

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An engine of a train, moving with uniform acceleration, passes the signal – post with velocity u and the last compartment with velocity υ . The velocity with which middle point of the train passes the signal post is:

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An engine of a train, moving with uniform acceleration, passes the signal – post with velocity u and the last compartment with velocity $υ .$ The velocity with which middle point of the train passes the signal post is: