Question
Tue September 25, 2012 By:

The speed of a train increases at a constant rate c from zero to v, and then remains constant for an interval and finally decreases to zero at a constant rate p.If L be the total distance travelled, then the total time taken is______. Choose the correct option.

Expert Reply
Thu September 27, 2012
time taken to accelerate to v:
 
t1 = v/c
 
time taken to decellerate:
 
t2 = v/p
 
distance travelled in these time intervals:
 
in t1:
s1 = v2/2c
 
in t2:
s2 = v2/2p
 
thus distance for which speed is constant:
s3 = L - v2/2(1/c + 1/p)
time taken for this:
t3 = s3/v = L/v - v/2(1/c+1/p)
 
total time taken:
 
t1+ t2+ t3
 
clearly no option match;
the correct answer is: L/v + v/2(1/c+1/p)
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