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Finding Average Velocity

The motor of ...

Question

The motor of an electric train can give it an acceleration of 1 m/s^2 and brakes can give it retardation of 3m/s^2. Find the shortest time in which train can make a trio between two stations 1215 m apart.

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Solution

Let the train accelerates upto a distance of 'x'm and then decelerate and stop after (1215-x)m.
So at a point x , the velocity (v) is given by v^2 = 0 + 2x .
This velocityis retarted with a deceleration of 3m/s^2.
So 2x = 23(1215-x).
This gives x = 911m.
So v^2 = 2x 911
v = 43 m/s.
Since, v = u + at ,
we get, 43= 0 + 1t
t = 43 s
Now for the decelerating journey ,
0 = 43- 3t
t =14 s.
So the total journey time = 43 + 14 = 57 seconds.

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