Question

The greatest acceleration of deceleration that the 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

Answer 1

Accn and declrcn each have taken time = t/2
S= 1/2(at/2)*t= at^2/4
t= 2√s/a

Answer 2

Given,

The greatest acceleration of deceleration that the train may have is a.

To find,

The minimum time in which the train can get from one station to the next at a distance s is?

Solution,

In this case, train should accelerate for half the distance and then decelerate. So, using equation of kinematics as :

$\dfrac{s}{2}=\dfrac{1}{2}at^2$

$t=\sqrt{\dfrac{d}{a}}$

Since, T = 2t

So,

$t=2\sqrt{\dfrac{d}{a}}$

So, the minimum time is $2\sqrt{\dfrac{d}{a}}$.