A train takes 2 minutes to acquire its full speed 60 kph from rest and 1 minute to come to rest from the full speed. If somewhere between two stations 2 km of the track is under repair with the speed

Question

A train takes 2 minutes to acquire its full speed 60 kph from rest and 1 minute to come to rest from the full speed. If somewhere between two stations 2 km of the track is under repair with the speed limited to 20 kph, find the late running of the train on account of the repair work. (Answer in seconds.)

TestHub · Accepted Answer

Acceleration a 1 ​ = 120 50/3 ​ = 36 5 ​ m / s 2 (2 min to 60 kph); retardation a 2 ​ = 60 50/3 ​ = 18 5 ​ m / s 2 (1 min from 60 kph). Slowing 60 → 20 kph: 40 s over 2 a 2 ​ ( 50/3 ) 2 − ( 50/9 ) 2 ​ = 444 m ; 2 km at 20 kph: 360 s; regaining 20 → 60 kph: 80 s over 889 m. Affected stretch = 444 + 2000 + 889 = 3333 m covered in 40 + 360 + 80 = 480 s; at full 60 kph the same stretch takes 50/3 3333 ​ = 200 s. Late running = 480 − 200 = 280 s = 4 min 40

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