Does anyone know the answer (s) to this?

  • MHB
  • Thread starter Jimmy Perdon
  • Start date
In summary, the power required to sustain the motion of an electric car at a certain speed experiencing nonzero drag can be modeled by the equation P = Av^2 + (B/v). To find the speed that minimizes the power, we set the derivative of this equation equal to 0 and solve for v, which is v = √(B/2A). The distance the car can travel at this speed is dependent on the usable store of energy, E.
  • #1
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)?
 
Physics news on Phys.org
  • #2
Here's the derivative for the function of power, \(\displaystyle P=Av^2+\frac{B}{v} (\text{Where }A\text{ and }B\text{ are positive constants)} \) that they give in the introduction to the problem:

\(\displaystyle P'(v)=2Av-\frac{B}{v^2} \)

To answer \(\displaystyle \text{(a) What speed }vP\text{ minimizes power?} \) we set this expression equal to \(\displaystyle 0 \) and solve for \(\displaystyle v \):

\(\displaystyle
\begin{align*}
2Av-\frac{B}{v^2}&=0 \\
2Av&=\frac{B}{v^2} \\
2Av\cdot\frac{v^2}{B}&=\frac{B}{v^2}\cdot\frac{v^2}{B} \\
\frac{2Av\cdot v^2}{B}&=1 \\
\frac{2Av^3}{B}\cdot\frac{B}{2A}&=1\cdot\frac{B}{2A} \\
v^3&=\frac{B}{2A} \\
v=\sqrt[3]{\frac{B}{2A}} \\
\end{align*}
\)

Now we need to determine if this result is a minimum or a maximum and we do this by examining the concavity of the graph of \(\displaystyle P \)

I'll let you take a look at the graph and experiment with the different values for \(\displaystyle A \) and \(\displaystyle B \). As a suggestion, take a look at the graph when \(\displaystyle A \) and \(\displaystyle B \) are different signs.[DESMOS]{"version":7,"graph":{"viewport":{"xmin":-10,"ymin":-7.65696784073507,"xmax":10,"ymax":7.65696784073507}},"randomSeed":"86f5ca9aa79de8cb0e8d39ee14441c5a","expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"P=2Av^{2}+\\frac{B}{v}"},{"type":"expression","id":"3","color":"#388c46","latex":"B=-1","hidden":true},{"type":"expression","id":"2","color":"#2d70b3","latex":"A=-1","hidden":true}]}}[/DESMOS]
 
Last edited:
  • #3
https://mathhelpboards.com/threads/does-anyone-know-the-answer-to-this.28654/
 

What does "this" refer to in the question?

"This" can refer to any specific question or problem that the person is seeking an answer to. It could be a scientific question, a math problem, or any other type of inquiry.

Why is the person asking if anyone knows the answer?

The person may be asking if anyone knows the answer because they have been unable to find it on their own and are looking for help. They may also be seeking confirmation from others to ensure that their answer is correct.

Is there a specific field or subject that the question pertains to?

The question could pertain to any field or subject, depending on the context. It could be related to biology, physics, history, or any other topic that requires knowledge and understanding.

What should I do if I know the answer to the question?

If you know the answer to the question, you can provide it to the person asking or direct them to a reliable source where they can find the answer. It is always helpful to share knowledge and help others find the answers they are seeking.

What if no one knows the answer?

If no one knows the answer, it may be necessary to do further research or consult with experts in the field. It is also possible that the answer may not be known yet and further study is needed. It is important to keep an open mind and continue seeking knowledge and understanding.

Suggested for: Does anyone know the answer (s) to this?

Replies
1
Views
637
Replies
4
Views
713
Replies
2
Views
831
Replies
2
Views
1K
Replies
9
Views
1K
Back
Top