# Does anyone know the answer to this?

• MHB
• Jimmy Perdon
In summary, the conversation discusses a simplified model for calculating the power required to sustain the motion of an electric car, with a specific focus on finding the minimum power and the distance the car can travel with a given amount of energy. This involves determining the optimal speed and using it to calculate the power and distance. The conversation also mentions that the topic is more suited for a calculus discussion rather than a chat room.
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)?

Jimmy Perdon said:
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.

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