Question

the two ends of train moving with a constant acceleration pass a certain velocities 5m/s and 12m/s,the velocity with which the middle point of the train passes the same point is​

Answer 1

Answer:

et  s be the length of train using v  

2 =u  

2 +2a×s  or 2as=v  2  −u  2       ......(1)

Where v is final velocity after travelling a distance s with an acceleration a and u is initial velocity as per question

Let velocity of middle point of train at same point is v  ′ , then (v  ′  )  2  =u  2 +2a×(s/2) =u  2 +as                      .....(2)

By equations (1) and (2), we get v  ′  =  2 v  2  +u  2

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Answer 2

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$v. = \sqrt{v {}^{2} + u {}^{2} \div 2 } \\ v. = \sqrt{12 {}^{2} + 5 {}^{2} \div 2 } \\ v. = \sqrt{144 + 25} \div 2 \\ v. = \sqrt{169 \div 2}$

$v. = 13 \div \sqrt{2} \\ v. = 13 \sqrt{2 } \div 2$