The position of a point in the – plane is given by the vector metres.

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

Problem

The position of a point in the

x

–

y

plane is given by the vector

\mathbf r(t)=3 t^{2}\,\hat{i}+2 e^{0.5 t}\,\hat{j}

metres. (a) Determine the instantaneous velocity vector at

t = 1\,\text{s}

. (b) Find the magnitude of this velocity at the same instant.