# Homework Help: Consistent Trajectory for a non-zero rest mass particle?

1. Feb 9, 2017

### DeldotB

1. The problem statement, all variables and given/known data
Good day all!
Quick question:
As part of a problem statement, i'm asked to verify if the trajectory: $$\frac{dx}{dt}=\frac{cgt}{\sqrt{1+g^2t^2}}$$
Is "consistent".

2. Relevant equations
None

3. The attempt at a solution

Im not sure what "consistent" means. Does it mean, $\frac {dx}{dt} < c$ for all t? If that's so, I run into a problem because in the limit as t approaches infinity, the velocity = the speed of light (the limit goes to c). Am I approaching this the wrong way? (The trajectory is supposed to be "consistent")

Last edited: Feb 9, 2017
2. Feb 9, 2017

### PeroK

You may want to check the limit of that expression for large $t$.

3. Feb 9, 2017

### DeldotB

PeroK: Not sure what you mean...
I get "c" as the limit. Maybe my work is wrong? $$Lim\, \, t\rightarrow \infty (\frac{cgt}{\sqrt{1+(9.8))^2t^2}})=cg(Lim\, \, t\rightarrow \infty (\frac{t}{\sqrt{1+(9.8))^2t^2}}))=cg(5/49)=c$$. So as t approaches infinity, the velocity approaches c.

4. Feb 9, 2017

### PeroK

That's correct, but inconsistent with the limit of $cg$ you gave in the original post!

5. Feb 9, 2017

### DeldotB

Ah, I see. A miss-type. Well, nevertheless, this trajectory doesn't seem to be consistent even though my assignment is saying it should be.