can someone explain how to do this question please!! (1 Viewer)

[iheartgeorge]

Does somebody tell me what steps i need to carry out to answer this please..
The cost of running a car at an average speed of v km/h is given by:
c= 150 + (v squared)/80 cents per hour
Find the average speed, to the nrs km/h at which the cost of a 500km trip is a minimum

 

[darkliight]

Somebody does not.

Are you sure you have typed the question correctly?

 

[word.]

cost = (150 + v^2/80) * time

velocity = displacement/time

c = (150 + 500^2/(80t^2))t
c = 150t + 3125/t

dc/dt = 150 - 3125/t^2

stat points occur when dc/dt = 0
i.e. when 3125/t^2 = 150 -> t^2 = 3125/150 = 125/6
t = ~4.56 (t > 0)

d/dt(dc/dt) = 3125/3t^3 > 0 (t > 0) so this is a minimum

when t = 4.56, v = 500/4.56 = 109.65km/h

 

[iheartgeorge]

thanks heaps!!