For a particle moves in the plane with constant acceleration vector

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

Problem

For

t\ge 0

a particle moves in the plane with constant acceleration vector

\mathbf a(t)=\langle 4,-3\rangle

. The following conditions are known: • Velocity at

t=2

\mathbf v(2)=\langle 10,5\rangle

. • Position at

t=1

\mathbf r(1)=\langle 6,-2\rangle

. Answer the questions below, showing all steps. (a) Determine the velocity vector

\mathbf v(t)

for

t\ge 0

. (b) Find the position vector

\mathbf r(t)

for

t\ge 0

. (c) Compute the position of the particle at

t=4

. Interpret the result in context.