Question

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

(1) \(\frac{u+v}{2}\)

(2) \(\frac{u^2+v^2}{u+v}\)

(3) \(\sqrt{u^2+v^2}\)

(4) \(\sqrt{\frac{u^2+v^2}{2}}\)

Answer 1

 (4) \(\sqrt{\frac{u^2+v^2}{2}}\)

Let the total length of the train be 2x. Let the velocity of the middle point of the train passing the pole be v_m. Then, for the first half of the journey of train,

For the second half part of the journey, we have;

Adding Eqns. (1) and (2) we have