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 in between two stations 1 km of the track be under repair and the limi

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 in between two stations 1 km of the track be under repair and the limited speed on this part be fixed to 20 kph, find the late running of the train on account of this repair work, assuming otherwise normal at running of the train between the stations. (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 ; 1 km at 20 kph: 180 s; regaining 20 → 60 kph: 80 s over 889 m. Affected stretch = 444 + 1000 + 889 = 2333 m covered in 40 + 180 + 80 = 300 s; at full 60 kph the same stretch takes 50/3 2333 ​ = 140 s. Late running = 300 − 140 = 160 s = 2 min 40

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