Question

At a distance of 400m from a traffic signal, brakes are applied to a locomotive to produce an retardation of 0.3m/s^2. Initial velocity of the locomotive is 54 km/hr.
Determine the position of the locomotive with respect to the traffic light after the application of brakes for 1 min.

Answer 1

Initial velocity, u = 54 km/h = 54×5/18 m/s = 15 m/s

Acceleration, a = -0.3 m/s^2

Time taken by the locomotive to come to rest is say ‘t’,

Using, v = u + at

=> 0 = 15 – 0.3t

=> t = 15/0.3 = 50 s

Thus, the locomotive comes to rest in 50 s which is less than 1 min.
So, to find the postion of the locomotive relative to the traffic light after 60 s we must find the distance traveled by the locomotive in 50 s.

Using,

S = ut + ½ at^2

=> S = 15×50 + ½ (-0.3) × 50^2

=> S = 750 – 375

=> S = 375 m

Thus, distance of the locomotive from the traffic light is = 400 – 375 = 25 m