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Consider a train which can accelerate with an acceleration of 20cm/sec2 and slow down with a deceleration of 100cm/sec2. Find the minimum time for the

train to travel between the stations 2.7 km apart.
Please help how to solve this problem. Thanku in advance.



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Let the train accelerate for t1 seconds when it starts from rest from 1st railway station and then decelerate for t2 seconds to stop at the next station. The train does not travel with uniform velocity in between.

Then Its maximum speed is v = u + a t = 0 + 0.20 t1
       So   v = 0.20 t1 m/sec
Again for the decelerating part:  v = u+at =>  0 = v - 1.00 t2    => v = t2
         so v = 0.20 t1 = t2
               t1 = t2/0.2 = 5 t2 

    so durations of accelerating phase and decelerating phase are inversely proportional to the magnitudes of acceleration.

distance traveled s = ut+1/2 a t²
Sum of the distances traveled in the two phases :
     0 t1 + 1/2 0.20 t1² + (t2)* t2 - 1/2 *1*t2² = 2700 meters
substitute the value of t1
         0.1 (5 t2)² + (t2)² - 1/2 (t2)² = 2700
         3 (t2)² = 2700
         t2² = 900          t2 = 30 sec        t1 = 150 sec

total time of travel between stations = 180 sec

2 5 2
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