A particle travels in the plane so that its position at time seconds is
MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
A particle travels in the plane so that its position at time t seconds is r(t)=⟨t2−4t,3t+2⟩, where distances are measured in meters.
(a) Determine the velocity vector and the speed of the particle when t=3.
(b) Find the acceleration vector for all t and state whether the acceleration is constant.
(c) Compute the magnitude of the displacement of the particle from t=1 to t=3. Show all work and include units.
(d) Is the particle ever at rest for t>0? Provide a full justification based on your results.