# Integrating Newton's Law

1. Aug 29, 2010

### bhsmith

1. The problem statement, all variables and given/known data
Starting from the modified Newton's Law

(dp(rel))/dt=F

with a constant Force F, and assuming that the particle starts with v=0 at time t=0, show that the velocity at time t is given by

V(t)=c [(Ft/mc)/(1+ Ft/mc)]

2. Relevant equations

3. The attempt at a solution
I know that I can integrate both sides of the equation with respect to time and solve, but i'm stuck on how to start that off. Any help would be appreciated!

2. Aug 29, 2010

### rpf_rr

Integrate, you find p=Ft, substitute p=mv/sqrt(1-v^2/c^2), some arithmetics and you fininshed, your solution is wrong, is valid for v^2

3. Aug 29, 2010

### bhsmith

I figured that one out too. But that equation for v(t) is stated in the problem. I'm thinking it might be different because it is supposed to be a "modified" Newton's Law for relativity instead of the classical equation P(class)=mv

4. Aug 30, 2010

### rpf_rr

my result is correct for relativity (at least for special as far i know), it is even reported in my textbook