Question 63: Motion in 1D

Question

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 :

Accepted Answer

Let initial speed of train u. When midpoint of the train reach the signal post it's velocity becomes v
0
.
$$ 	herefore $$ $$v_0^2 = {u^2} + 2as$$ .......(1)
When train passes the signal post completely it's velocity becomes v.
$$ 	herefore $$ $${v^2} = v_0^2 + 2as$$ ......(2)
Subtracting (2) from (1) we get,
$$v_0^2 - {v^2} = {u^2} - v_0^2$$
$$ \Rightarrow v_0^2 + v_0^2 = {u^2} + {v^2}$$
$$ \Rightarrow {v_0} = \sqrt {{{{u^2} + {v^2}} \over 2}} $$

Answer

$${{u + v} \over 2}$$

Answer

$$\sqrt {{{{v^2} - {u^2}} \over 2}} $$

Answer

$${{v - u} \over 2}$$

Answer

$$\sqrt {{{{v^2} + {u^2}} \over 2}} $$

Motion in 1D

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 :

Choose the correct answer: