MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
A point mass moves in the plane. Its velocity vector at time t seconds is v(t)=⟨e2t,t2−4t+1⟩, where components are measured in meters per second.
(a) Find the acceleration vector a(t).
(b) Determine the magnitude of the acceleration at t=1 and state the units.
(c) Find all times t for which the acceleration vector is orthogonal to the velocity vector. Show all work.
(d) Explain what orthogonality of velocity and acceleration implies about the particle’s speed at the times found in part (c).