Question

If a train travelling at $30\text{m/s}$ is to be brought to rest in a distance of $200\text{m}$, then its retardation should be

• A. $4.25{\text{m/s}}^2$
• B. $2.50{\text{m/s}}^2$
• C. $2.25{\text{m/s}}^2$
• D. $3.50{\text{m/s}}^2$

Answer 1

The correct option is C $2.25{\text{m/s}}^2$

As per the question, final velocity of the train will be $v=0$
Given, initial velocity $u=30\text{m/s}$, distance $s=200\text{m}$
As per $3^{rd}$ equation we have
$v^2-u^2=2as$
$\Rightarrow 0-{30}^2=2a\times 200\Rightarrow a=\frac{-900}{400}=-2.25{\text{m/s}}^2$
Thus, the retardation of the train is $2.25{\text{m/s}}^2$