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

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Homework Help Overview

The discussion revolves around deriving the velocity formula V(t) from a modified version of Newton's Law, specifically in the context of relativistic mechanics. The original poster presents a problem statement involving the integration of a force equation with a constant force and initial conditions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the integration of the modified Newton's Law and the implications of using relativistic equations. There is a focus on how to correctly apply the equations and whether the provided velocity formula aligns with the principles of relativity.

Discussion Status

Some participants have offered insights into the integration process and the relationship between momentum and velocity in a relativistic context. There are differing views on the validity of the original poster's approach and the correctness of the velocity formula provided in the problem statement.

Contextual Notes

Participants are navigating the complexities of modified Newton's Law as it applies to relativistic scenarios, questioning the assumptions made in the problem setup and the definitions of momentum and velocity in this framework.

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

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