You and your best friend Janine decide to play a game. You are in a land of make believe where you are a function, $f(t)$, and she is a function, $g(t)$. The two of you move together throughout this land with you (that is, $f(t)$ ) controlling your East/West movement and Janine (that is, $g(t)$ ) controlling your North/South movement.

If your identity, $f(t)$, is given by $$f(t) = \frac{(t^2 + 14)^{\frac{3}{2}}}{3}$$ and Janine's identity, $g(t)$, is given by $$g(t) = 7 t$$ then how many units of distance do the two of you cover between the Most Holy Point o' Beginnings, $t=0$, and The Buck Stops Here, $t=26$?

We travel units of distance.