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At a distance L = 400m away from the sig...

At a distance L = 400m away from the signal light, brakes are applied to a locomotive moving at a velocity u = 54 km/h. Determine the position of rest of the locomotive relative to the signal light after 1 min. of the application of the brakes if its acceleration a = `-0.3m//s^(2)`.

Text Solution

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Since the locomotive moves with a constant deceleration after the application of brakes, it will come to rest in "t" sec.
We know, v = u + at
Here u = 54km/h = `54xx5//18` = 15m/s , v = 0 for given situation and given a = `-0.3m//s^(2)`
We get, `t=(-15)/(-0.3)=50s`
During which it will cover a distance `s=(-u^(2))/(2a)=375m`.
Thus in 1 min after the application of brakes the locomotive will be at a distance l = L - s = 400 - 375 = 25 m from the signal light.
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