the cost of fuel for running a train is proportional to square of speed generated in km/h.it cost rs 48/h when the train is moving at speed of 16km/h.what is its economical speed if the fixed charges are rs 300/hour over and above the running cost!
let F= fuel cost V= speed and K= constant
F=KV2
for the given condition, 48= K x 162
=) K= 3/16
as fixed charge is in Rs/hr, it is proportional to 1/V. (time= distance/velocity)
for minima fuel cost, dF/dV = 0
=) d/dV (KV2 + A/V) A= rs 300/ hr
=) 2KV - A/V2 = 0
=) 2KV = A/V2
=) V3 = A/(2*(3/16)) = 300/(3/8)=800
=) V = 9.28 kmph
F=KV2
for the given condition, 48= K x 162
=) K= 3/16
as fixed charge is in Rs/hr, it is proportional to 1/V. (time= distance/velocity)
for minima fuel cost, dF/dV = 0
=) d/dV (KV2 + A/V) A= rs 300/ hr
=) 2KV - A/V2 = 0
=) 2KV = A/V2
=) V3 = A/(2*(3/16)) = 300/(3/8)=800
=) V = 9.28 kmph