First slide

The 3 equation for uniform acc

Question

A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. Then, which amongst the following option is correct about the relation between the distance covered by the boggy and distance covered by the train in the same time?

Moderate

A

Both will be equal
B

First will be half of second
C

First will be 1/4 of second
D

No definite ratio

Solution

Let a be the retardation of boggy, then distance covered by it be s_b. If u is the initial velocity of boggy after detaching
from train (i.e. uniform speed of train)
$v^{2} = u^{2} + 2 a s \Rightarrow 0 = u^{2} - 2 a s$
$\Rightarrow$ $s_{b} = \frac{u^{2}}{2 a}$
Time taken by boggy to stop
$v = u + a t \Rightarrow 0 = u - a t \Rightarrow t = \frac{u}{a}$
In this time t, distance travelled by train, $s_{t} = u t = \frac{u^{2}}{a}$
Hence, ration $\frac{s_{b}}{s_{t}} = \frac{1}{2} .$

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