The two ends of a train moving with constant acceleration pass a certain point with velocities u and v. The velocity with which the middle point of the train passes the same point is

Question

The two ends of a train moving with constant acceleration pass a certain point with velocities u and v. The velocity with which the middle point of the train passes the same point is (A) (u + v)/2 (B) (u2 + v2)/2 (C) √(u2 + v2)/2 (D) √u2 + v2

Tardigrade Admin · Accepted Answer

Let the length of train is s, then by third equation of motion,

v^{2} = u^{2} + 2 a \times s

....(1)
Where v is final velocity after travelling a distance s with an acceleration a & u is initial velocity as per question
Let velocity of middle point of train at same point is v', then

(v^{'})^{2} = u^{2} + 2 a \times (s /2)

....(2)
By equation (1) & (2), we get

v^{'} = \frac{v ^{2} + u ^{2}}{2}

Q. The two ends of a train moving with constant acceleration pass a certain point with velocities u and v. The velocity with which the middle point of the train passes the same point is

$(u + v) /2$

$(u^{2} + v^{2}) /2$

$(u^{2} + v^{2}) /2$

$u^{2} + v^{2}$

Q. The two ends of a train moving with constant acceleration pass a certain point with velocities u and v. The velocity with which the middle point of the train passes the same point is

(u+v)/2

(u2+v2)/2

(u2+v2)/2​

u2+v2​

$(u + v) /2$

$(u^{2} + v^{2}) /2$

$(u^{2} + v^{2}) /2$

$u^{2} + v^{2}$