A rocket is fired from rest at $x=0$ and travels along a parabolic trajectory described by $y^2=[150({10}^3)x]m.$

Part A

If the $x$ component of acceleration is $a_x=(\frac{1}{5}{t}^2)\frac{m}{s^2},$ where $t$ is in seconds, determine the magnitude of the rocket's velocity when $t=8s.$

Express your answer using three significant figures and include the appropriate units.