A particle moves in the plane with velocity vector

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

Problem

\mathbf v(t)=\langle f(t),g(t)\rangle

. At time

t=1

the particle is located at

\mathbf r(1)=\langle 3,5\rangle

. Which of the following expressions gives the particle’s

y

–coordinate at time

t=4

? (a)

5+\displaystyle\int_{1}^{4}|g(t)|\,dt

(b)

5+\displaystyle\int_{1}^{4} g(t)\,dt

(c)

3+\displaystyle\int_{1}^{4} g(t)\,dt

(d)

5+\displaystyle\int_{0}^{4} g(t)\,dt