An engine of a train, moving with uniform acceleration, passes the...

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity

u

and the last compartment with velocity

v

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

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment

Options

A $\dfrac{u + v}{2}$
B $\sqrt{\dfrac{{v}^{2} + {u}^{2}}{2}}$
C $\dfrac{v - u}{2}$
D $\sqrt{\dfrac{{v}^{2} - {u}^{2}}{2}}$

Correct answer

B. $\sqrt{\dfrac{{v}^{2} + {u}^{2}}{2}}$

Step-by-step solution

${\left(v '\right)}^{2} = {u}^{2} + 2ad$

${v}^{2} = {\left(v '\right)}^{2} + 2ad$

solving, we get

$v ' = \sqrt{\dfrac{{v}^{2} + {u}^{2}}{2}}$

An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment

Practice Motion in One Dimension on Quantrex Academy →

More from Motion in One Dimension

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a… JEE Main 2026 Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12… JEE Main 2026 The velocity ( v ) versus time ( t ) plot of a particle is shown in the figure, for a… JEE Main 2026 From 18 m height above the ground a ball is dropped from rest. The height above the… JEE Main 2026 Two cars A and B are moving in the same direction along a straight line with speeds 100… JEE Main 2026 The velocity of a particle is given as v = -x i + 2y j - z k m/s. The magnitude of… JEE Main 2026 A particle starts moving from time t=0 and its coordinate is given as x(t)=4 t^ 3 -3 t A.… JEE Main 2026 Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the… JEE Main 2026 Full Motion in One Dimension list All JEE Main PYQs