Question

The two ends of a train moving with constant acceleration pass a certain point with velocities u and 3u. The velocity with which the middle point of the train passes the same point is ___________ ?

Answer 1

Answer on Question #52771, Physics, Mechanics | Kinematics | Dynamics

The two ends of a train moving with constant acceleration pass a certain point with velocities $u$ and $3u$. The velocity with which the middle point of the train passes the same point is __________?

Solution:

The train is accelerating, so we can use the formula's for accelerated motion in one line:

$$v^2 - u^2 = 2aL$$

u = head of train

3u = tail of train [v = 3u]

so

$$(3u)^2 - u^2 = 2aL$$ $$9u^2 - u^2 = 2aL$$ $$8u^2 = 2aL$$ $$a = \frac{4u^2}{L}$$

Now at middle of train

$$L' = \frac{L}{2}$$ $$v'^2 - u^2 = 2aL'$$ $$v'^2 = u^2 + \frac{2aL}{2}$$

put the value of a

$$v'^2 = u^2 + 2 * \frac{4u^2}{L} * \frac{L}{2}$$ $$v'^2 = 5u^2$$ $$v' = u\sqrt{5}$$

Answer: $u\sqrt{5}$

http://www.AssignmentExpert.com/