# Velocity and Mass to Acceleration

1. Feb 25, 2015

### Zales

I am graphing an equation, but my software will not graph more than two variables. I have velocity (v) and velocity dependent mass (m sub 0), but I need to write it in terms of x, which I have as acceleration. This problem stems from me plugging in the following equation for the relationship between speed and mass: (m sub 0)/sqrt(1-((v/c)^2). If it is even possible to do it another way, please let me know. Or if it's not possible and I need better software, please let me know is that is the case also.

Thank you,
Zales

PS. This post is very poorly worded. Here is a link to a much better formatted equation, and if you wish for me to clarify anything, please let me know.

2. Feb 25, 2015

### Mentallic

You'll have a much more clear picture of what's happening if you choose your variable to be v, and set c=3x108 and m0 to be a parameter that you change to whatever you like. Better yet would be to choose your variable to be v/c which means to set c=1 and then v will be represented by a percentage of c. So at x=0.5 on the graph, that means that v will be half of the speed of light.

3. Feb 26, 2015

### Zales

Sorry, maybe I should have added more information. What I'm trying to graph is F=Ma, with 'F' as y, 'M' as the slope, and 'a' as 'x'. In slope intercept form, I had F=Ma+0. The equation is equivalent to 'M', so the equation was plugged in for 'M'. I have 'c' as 2.998x10^8. My full equation, so far, is y=(m/(sqrt(1-(v/(2.998*10^8))^2)))x+0.

PS. How did you input your subscripts and superscripts?

4. Feb 26, 2015

### Mentallic

You may want to head over to the physics section of the forum as well to get a better idea of what your equations should actually be, because relativistic mass increases in a stationary reference frame as v approaches c, so it's not quite as simple as that. In 1 dimension (to keep things simple for the moment) your equation would be

$$F=\gamma ^3m_0a$$

where a is simply the change in velocity over time, $a=\frac{dv}{dt}$ and $\gamma$ is the lorentz factor $\gamma=\frac{1}{\sqrt{1-v^2/c^2}}$

It gets more complicated in 3 dimensions though. You'll have situations where the particle won't accelerate in the direction you applied the force, which is very counter-intuitive with respect to Newtonian mechanics.