The motors of an electric train can give it an acceleration of 1 ms-2 and the brakes can give a negative acceleration of 3 ms-2. What is the shortest time in which the train can make a trip between two stations 1350 m apart?
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your answer is 36.74 sec
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Answer:
45s
Explanation: let s1 be the distance travelled by the train moving with acceleration 1 m/s^2 for time t1 and s2 be the distance travel by the train moving with retardation 3 m/s^2 for time t2 . if v is the velocity of the train after time t1 , then
v = 1 x t1 .....(i)
s1 = 1/2 x 1 x t1^2 .....(ii)
also, v = 3t^2 .....(iii)
and s2 = vt2 - 1/2 x 3 x t2^2
=t1 x t2 - 3/2 t2^2
from (i) and (iii)
t1 = 3 t2 or t2 = t1/3
s1 + s2 = (t1^2)/2 + t1 x t1/3 - 3/2 x (t1^2)/9 = 2/3 t1^2
1350 = 2/3 t1^2
t1 = 45 s
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