Using a simple model of constant acceleration 0.25 m s^-2, a researcher predicts that the velocity of the AUV exactly 80 seconds after being released from rest is 20 m s^-1. Show how the researcher has obtained this prediction.

Using a refined model that accounts for fluid resistance, it is assumed that the AUV's acceleration, $a{m\; s}^{-2}$, at time $t$ seconds after release is given by

where $v{m\; s}^{-1}$ is the velocity of the AUV at time $t$. Find an expression for $v$ in terms of $t$.

Compare the behavior of $v$ as $t\to \infty$ for both models.