A particle’s position in metres at time seconds is given by r(t)= t^ 2 , ,4t, ,5
MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
A particle’s position in metres at time t seconds is given by
r(t)=⟨t2,4t,5⟩.
The particle begins its motion at t=0.
(a) Determine the particle’s velocity vector v(t).
(b) Find all values of t≥0 at which the particle’s velocity is perpendicular to its position vector.
(c) Verify your answer to part (b) by explicitly evaluating the relevant dot product at each identified time.
(d) Describe the physical significance of the result from part (b) in the context of the particle’s motion.