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  • An engine of train, moving with uniform acceleration, passes the signal -post with velocity u and last compartment with velocity v. The velocity with which middle point of the train passes the signal post is: Option: 1 <img alt=

An engine of train, moving with uniform acceleration, passes the signal -post with velocity u and last compartment with velocity v. The velocity with which middle point of the train passes the signal post is:
Option: 1 \sqrt{\frac{v^2-u^2}{2}}
Option: 2 \frac{u+v}{2}
Option: 3 \frac{u-v}{2}
Option: 4 \sqrt{\frac{v^2+u^2}{2}}

Answers (1)

best_answer

a = uniform acceleration

u = velocity of first compartment

v = velocity of last compartment

2d= length of the train

C= middle point of the train

Now using 3rd equation of motion

\mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}

we get

 \left(\mathrm{v}^{\prime}\right)^{2}=\mathrm{u}^{2}+2 \mathrm{ad}
and \mathrm{v}^{2}=\left(\mathrm{v}^{\prime}\right)^{2}+2 \mathrm{ad}

On solving both, we get
 
\mathrm{v} ^{\prime}=\sqrt{\frac{\mathrm{v}^{2}+\mathrm{u}^{2}}{2}}
 

Posted by

avinash.dongre

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