Consistent Trajectory for a non-zero rest mass particle?

[DeldotB]

Homework Statement

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".

Homework Equations

None

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")

 

[PeroK]

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

 

[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.

 

[PeroK]

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

 

[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.