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1. Sep 8, 2015

### mch

I'm new to this site, so please bear with me.

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

A particle of mass m has speed v(x) = α/√x. Calculate the force F(x) responsible. Then, calculate the displacement x(t) of the particle.

2. Relevant equations

The equations that I believe we are supposed to use are f=ma and f=m*dv/dt

3. The attempt at a solution

Since F= m*dv/dt, i tried this:

F = m*dv/dx*dx/dt = mv*dv/dx = -mvα/(2(x)^(3/2))

And that's as far as I could get for the first problem. However, this seems off because the force is in terms of two variables, right? V and x?

2. Sep 8, 2015

### Orodruin

Staff Emeritus
You already know v as a function of x so it is really only one variable ...

3. Sep 8, 2015

### vela

Staff Emeritus
You're given an expression for v in terms of x...

4. Sep 8, 2015

### mch

Oh okay great! So F(x) = -mα^2/(2x^2). Thank you! How silly of me.

So now I need to find x(t). Do i say that F = -mα^2/(2x^2) = mx'' and solve the second order differential equation? My initial conditions are that v(x=0) = 0 and x(t = 0)=0.

5. Sep 8, 2015

### Orodruin

Staff Emeritus
Those initial conditions are incompatible with v(x) = α/√x.

6. Sep 8, 2015

### Orodruin

Staff Emeritus
Also, you do not need to use the force equation, you already know that dx/dt = v(x) so you can just integrate this.

7. Sep 8, 2015

### mch

Thank you. I figured this out and I believe I got all the right answers.

Thanks a lot for your help!