# Work with Relation to Velocity

1. Feb 27, 2017

### Eeeff

1. The problem statement, all variables and given/known data
Help. If

w = F dx
where w is work, f is force and x is displacement, and also
F = k1v2
where force is a quadratic function of velocity v times a constant k1,
what would be work with regards to velocity?

2. Relevant equations
More info if needed.

v =a dt
a = k2 - k1v2/m

k2 is another constant representing the initial acceleration, and m is the mass of the object.

3. The attempt at a solution

I have some attempts but I am just clueless.

Thanks.

2. Feb 27, 2017

### Arman777

I have an idea.F is a funtion of v so W=∫F(v)dx the main purpose should be solve this integral but for that it must be in the same "thing".Like ∫tdt or ∫vdv etc.
Using a = k2 - k1v2/m and some equations you can find it.

3. Feb 27, 2017

### kuruman

I don't see where you got this. If F = ma and F = k1v2, what is a?

4. Feb 27, 2017

### haruspex

There is a very useful formula for when you don't care about the time of the motion:
$a=\frac{dv}{dt}=\frac{dx}{dt}\frac{dv}{dx}=v\frac{dv}{dx}$.

5. Feb 27, 2017

### kuruman

There is also the work-kinetic energy theorem.

6. Feb 27, 2017

### Eeeff

Let me clarify, Fext = k1v2. Fnet = ma = mk2 - Fext.

7. Feb 27, 2017

### Eeeff

Last edited: Feb 27, 2017
8. Feb 27, 2017

### kuruman

How many forces are there? If there is only one, the net force, i.e. the sum of all the forces, is that one force.

9. Feb 27, 2017

### Eeeff

Sorry for not making this clear. There is forceext1 = k1v2 that is acting against the object and constant forceext2 = mk2 acting on the object.

10. Feb 27, 2017

### kuruman

OK. The work done by which force is the question asking you to calculate?

I know you are new to PF, but for future reference, please post the problem exactly as it is given to you. It will avoid misunderstandings and your question will be answered more quickly.

11. Feb 27, 2017

### Eeeff

I wish to know the work done by F ext1. Anyway, why would I want to know the force done by the constant force, when it is just W = Fd.

12. Feb 27, 2017

### kuruman

It's not what you want to know, it's what the problem is asking you to answer. Actually, for this problem, finding the work done by the constant force is part of the answer. You can use the hint provided by haruspex (post#4) or by me (post #5); they are basically the same idea for tackling the problem.

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