A particle has velocity and acceleration

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A particle has velocity v(t)=⟨e2t, 2e2t, 3⟩\mathbf v(t)=\langle e^{2t},\,2e^{2t},\,3\rangle and acceleration a(t)=⟨2e2t, 4e2t, 0⟩\mathbf a(t)=\langle 2e^{2t},\,4e^{2t},\,0\rangle. Determine whether the particle’s speed is increasing, decreasing, or constant at t=0t=0.

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