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 pared passes the same point is
(1)2u
(2)3/2u
(3)√5u
(4)√10u

Answer 1

Answer on Question #54925, 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 pared passes the same point is

(1) $2u$

(2) $3/2u$

(3) $V5u$

(4) $V10u$

Solution:

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

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

where $L$ is length of train

$u$ = head of train velocity

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

Thus,

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

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 $a$

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

Answer: (3) $V5u$

http://www.AssignmentExpert.com/