For , the velocity of a particle is given by…

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

Problem

For

0\le t\le 4

, the velocity of a particle is given by

\mathbf v(t)=\langle 3t^{2},\,4t\rangle

. (a) Determine the particle’s speed at

t=1

. Show your work. (b) Determine the particle’s speed at

t=2

. (c) Compare the answers from parts (a) and (b) to decide whether the particle is moving faster at

t=1

or at

t=2

. Justify your conclusion numerically.