MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
A particle moves in space with velocity v(t)=⟨3t2,4sint,0⟩, where t is measured in seconds and the components are in meters per second. At time t=0 the particle is located at the point (2,−1,3).
(a) Determine the position vector r(t) for all real t.
(b) Evaluate the particle’s position at t=2 seconds.