A particle moves in the plane with velocity vector

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A particle moves in the plane with velocity vector v(t)=⟨a(t),b(t)⟩\mathbf v(t)=\langle a(t),b(t)\rangle. Explain how the definite integral of v(t)\mathbf v(t) on an interval [p,q][p,q] is related to the particle’s change in position over that same interval.

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