Train Velocity: Calculating Midpoint Velocity at Instant

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To determine the midpoint velocity of a train when the engine has an initial velocity 'u' and the last coach crosses a pole at velocity 'v', basic kinematic equations can be applied. The midpoint velocity can be calculated as an average of the initial and final velocities of the train. Since the guard's coach is moving at 'v', it suggests that the velocity of the midpoint will be influenced by both 'u' and 'v'. The assumption that the midpoint velocity equals 'v' is incorrect without considering acceleration or deceleration. Therefore, the correct approach involves using the average of the two velocities to find the midpoint velocity at that instant.
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1. If a train engine is traveling with initial velocity 'u' and the guard's coach(last coach of the train) is found to cross a pole with velocity 'v', then what is the velocity of the midpoint of the train at that instant?
 
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mayurkhairnar said:
1. If a train engine is traveling with initial velocity 'u' and the guard's coach(last coach of the train) is found to cross a pole with velocity 'v', then what is the velocity of the midpoint of the train at that instant?

What have you tried so far?
 
I have not tried anything. This question is asked my brother. He is appearing in Competitive exam
 
try using basic equations like v=u+at. i think that v will be same.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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