Answer
$x=4+4t; y=3+2t; z=8+12t$
Work Step by Step
We know that the velocity and acceleration is defined as: velocity is given as: $v(t)=r'(t)$ and acceleration is given as: $a(t)=v'(t)$
Now,$v(t)=\lt 2t,2,3t^2\gt \\ \implies v(2)=\lt 4,2,12 \gt$
Thus, we have the velocity components $v_x=4,v_y=2,v_y=12$
Now, the parametric equations are as follows:
$x=(4)(t)+4=4+4t; y=3+2t; z=(12)t+(8)=8+12t$
Thus, $x=4+4t; y=3+2t; z=8+12t$
