APFIVE Particle Position From Velocity Vector
A particle moving in the $$xy$$-plane has a velocity vector given by $$\displaystyle \mathbf{v}(t) = \left\langle \frac{1}{t+1}, t e^{-t} \right\rangle$$ for time $$\displaystyle t \ge 0$$. If the particle’s position is $$\displaystyle (-1, 2)$$ at time $$\displaystyle t=0$$, what is its distance from the origin at time $$\displaystyle t=2$$?
A
$$\displaystyle 1.847$$
B
$$\displaystyle 2.596$$
C
$$\displaystyle 3.225$$
D
$$\displaystyle 4.183$$
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