The speed of a train increases at a constant rate from alphazero to v, and then remains constant for an interval, and finally decreases to zero at a constant ratebeta . If L be the total distance travelled , then the total time taken is 

Asked by Petulla Mishra | 4th Nov, 2015, 10:06: AM

Expert Answer:

Time taken to accelerate to v:
 
t1 = v/α
 
Time taken to decellerate:
 
t2 = v/β
 
Distance travelled in these time intervals:
 
In t1:
s1 = v2/2α
 
In t2:
s2 = v2/2β
 
Thus, distance for which speed is constant:
s3 = L - v2/2(1/α + 1/β)

Time taken for this:
t3 = s3/v = L/v - v/2(1/α+1/β)
 
Total time taken:
 
t1+ t2+ t3 = L/v + v/2(1/α+1/β)

Answered by Yashvanti Jain | 4th Nov, 2015, 11:56: AM