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.

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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