A particle moves in the plane with position vector and velocity vector

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A particle moves in the plane with position vector r(t)\mathbf r(t) and velocity vector v(t)=r′(t)\mathbf v(t)=\mathbf r'(t). Which of the following expressions gives the particle’s net displacement vector from t=2t=2 to t=5t=5? (a) 3 v(5)3\,\mathbf v(5) (b) ∫25v(t) dt\displaystyle\int_{2}^{5}\mathbf v(t)\,dt (c) r(5)+r(2)2\displaystyle\frac{\mathbf r(5)+\mathbf r(2)}{2} (d) r(5)+r(2)\mathbf r(5)+\mathbf r(2)

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