A train takes 5minutes to cover a distance of 3km between two stations P & Q . Starting from rest at P , it accelerates at a constant rate to a speed of 40Km/h and maintains this speed until it is brought uniformly to rest at Q . If the train takes three times as long to decelerate as it does to accelerate , find the time taken by train to accelerate .
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40 km/h = 0.278 m/s
If it accelerated at a m/s^2, then it took t=0.278/a seconds to achieve that speed.
The distance covered while accelerating/decelerating is thus
1/2 at^2 + 0.278(3t) - 1/2 (a/3)(3t)^2
= 1/2 a(0.278/a)^2 + 0.278(3(0.278/a))-1/2 (a/3)(3(0.278/a))^2
= 0.155/a
Now, if it travels at constant speed for x seconds, we have
0.155/a + 0.278x = 3000
4(0.278/a) + x = 300
If it accelerated at a m/s^2, then it took t=0.278/a seconds to achieve that speed.
The distance covered while accelerating/decelerating is thus
1/2 at^2 + 0.278(3t) - 1/2 (a/3)(3t)^2
= 1/2 a(0.278/a)^2 + 0.278(3(0.278/a))-1/2 (a/3)(3(0.278/a))^2
= 0.155/a
Now, if it travels at constant speed for x seconds, we have
0.155/a + 0.278x = 3000
4(0.278/a) + x = 300
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