AP Calculus BC 9.5 Integrating Vector Valued Functions Questions

Review parametric position by integrating velocity components and using initial conditions to determine coordinates at a specified parameter value.

Covered syllabus points

FUN-8.A—Determine a particular solution given a rate vector and initial conditions

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At time $t \geq 0$ , a particle moving along a curve in the x y-plane has position (x(t), y(t)) with velocity vector $v(t)=\left(\cos \left(t^{2}\right), e^{0.5 t}\right)$ . At t=1, the particle is at the point (3,5).

Find the x-coordinate of the position of the particle at time t=2.

$x(2)=3+\int_{1}^{2} \cos \left(t^{2}\right) d t=2.557($ or 2.556 )

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Covered syllabus points

Question 1