Motion under a constant force (relativity-related)

[nastassja]

Homework Statement

Use the first order Taylor approximation (1 + \epsilon)ⁿ \approx 1 + n\epsilon for \epsilon<<1

to see what the particle's speed v(t) is in the non-relativistic limit of small speeds. The specific approximation you'll want to make is that the dimensionless quantity (Ft/m₀c) is much less than 1. Show that for very small values of this quantity, the particle's acceleration is constant, and find out what this acceleration is.

Homework Equations

\frac{1}{\sqrt{\frac{1}{Ft/m_{0}}+\frac{1}{c^{2}}}}

The Attempt at a Solution

I'm not sure what the question is asking. Do I use F=ma, and solve for a using the formula? How do I show that it works with Newtonian mechanics? Also, Do I take a limit as \epsilon approaches zero or...what? I don't think I'll have a problem doing the math, I'm just not clear about what is being asked.

Oh, and does epsilon = Ft/mc or just Ft/m? Because Ft/mc isn't in the equation and if I solve for it, the equation may become more complicated to solve for.

 

[CompuChip]

You do precisely what the question says; make an expansion of the square root. So first rewrite your expression to something containing
\frac{1}{(1 + \epsilon)^n}
where \epsilon is some quantity which you know is small (one is given in the question, big chance that will be your epsilon).

Don't worry about what epsilon will be, you'll see it roll out of the equation. Just focus on getting a form which you can expand.