Q. 214.4( 7 Votes )

# Consider a train which can accelerate with an acceleration of 20cm/s^{2} and slow down with deceleration of 100cm/s^{2}. Find the minimum time for the train to travel between the stations 2.7 km apart.

Answer :

Given, total distance need to cover, d = 2.7km = 270000 cm

Let distance covered in accelerated motion be d_{1} and distance covered in decelerated motion be d_{2}.

So, d_{1} + d_{2} = d …(1)

Now for d_{1}, initial velocity will be 0, and acceleration a = 20 cm/s^{2} and let final velocity be v.

Then,

Now for d_{1}, initial velocity will be v, and acceleration a’ = 100 cm/s^{2} and velocity will be 0.

Then,

Now putting values of d, d_{1} and d_{2} in equation (1), we get

And also for d_{1,} let the time taken to travel be t_{1} then

And also for d_{2,} let the time taken to travel be t_{2} then

Now total time to travel will be t_{1} + t_{2}

Rate this question :

Consider a train which can accelerate with an acceleration of 20cm/s^{2} and slow down with deceleration of 100cm/s^{2}. Find the minimum time for the train to travel between the stations 2.7 km apart.