A particle moves in the plane with velocity

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

Problem

A particle moves in the plane with velocity v(t)=⟨3t2,−2⟩\mathbf v(t)=\langle 3t^{2},-2\rangle. Given that its position at t=1t=1 is r(1)=⟨4,5⟩\mathbf r(1)=\langle 4,5\rangle, determine the position vector r(t)\mathbf r(t) for all tt.

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