MHB Does anyone know the answer to this?

[Jimmy Perdon]

A simplified model of the power P required to sustain the motion of an electric car at speed v experiencing nonzero drag can be modeled by the equation:

P = Av^2 + (B/v)
(where A and B are positive constants.)

(a) What speed vP minimizes power?
(b) What power does the speed in (a) require?
(c) Suppose that an electric car has a usable store E of energy. How far dP can the electric car travel at the
speed found in (b)?

 

[skeeter]

A simplified model of the power P required to sustain the motion of an electric car at speed v experiencing nonzero drag can be modeled by the equation:

P = Av^2 + (B/v)
(where A and B are positive constants.)

(a) What speed vP minimizes power?
(b) What power does the speed in (a) require?
(c) Suppose that an electric car has a usable store E of energy. How far dP can the electric car travel at the
speed found in (b)?

(a) find $\dfrac{dP}{dv}$, set it equal to zero, and determine the value of velocity that minimizes power.

(b) substitute the value of velocity found in part (a) into the original power equation

(c) Power is a rate of energy use over time. At the velocity found in part (a), time will be a maximum for a fixed value of available energy, E.

$P = \dfrac{E}{t} \implies t = \dfrac{E}{P}$, and distance traveled is $d = v \cdot t$why is this posted in the chat room? should be in calculus.