# Consider a train which can accelerate with an acceleration of 20cm/s2 and slow down with deceleration of 100cm/s2. Find the minimum time for the train to travel between the stations 2.7 km apart.

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

Let distance covered in accelerated motion be d1 and distance covered in decelerated motion be d2.

So, d1 + d2 = d …(1)

Now for d1, initial velocity will be 0, and acceleration a = 20 cm/s2 and let final velocity be v.

Then,

Now for d1, initial velocity will be v, and acceleration a’ = 100 cm/s2 and velocity will be 0.

Then,

Now putting values of d, d1 and d2 in equation (1), we get

And also for d1, let the time taken to travel be t1 then

And also for d2, let the time taken to travel be t2 then

Now total time to travel will be t1 + t2

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