How Does Integrating Modified Newton's Law Lead to the Velocity Formula V(t)?

[bhsmith]

Homework Statement

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)]

Homework Equations

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!

 

[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

 

[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

 

[rpf_rr]

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