Question

The greatest acceleration or deceleration that a train may have is $a$. The minimum time in which the train can get from one station to the next at a distance $s$ is:

• A. $\sqrt{\frac{s}{a}}$
• B. $\sqrt{\frac{2s}{a}}$
• C. $2\sqrt{\frac{s}{a}}$
• D. $\frac{1}{2}\sqrt{\frac{s}{a}}$

Answer 1

The correct option is C $2\sqrt{\frac{s}{a}}$

The time will be minimum if it get accelerated to half distance then other hall distance let retreated

So using $s=ut+\frac{1}{2}a{t}^2$ ; $u=0$ (initially at rest)

We have $\frac{s}{2}=\frac{1}{2}a{t}_1^2$

$\Rightarrow t_1=\sqrt{\frac{s}{a}}$ it is time to cover half $(i.e\frac{s}{2})$ distance with acceleration $a$

other half $\left(\frac{s}{2}\right)$ in all be covered in same time because retarelation is also a so total time $t=2t_1=2\sqrt{\frac{s}{a}}$

Option $C$ is correct