A particle travels along a horizontal track so that its velocity vector for seconds…

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

Problem

A particle travels along a horizontal track so that its velocity vector for

0\le t\le 5

seconds is given by

\mathbf v(t)=\langle 6-2t,3\rangle

, where the

x

–component is in meters per second and the constant

y

–component is in meters per second. (a) Determine each time in

0\le t\le 5

at which the particle changes direction in the

x

–direction. (b) For each sub-interval of time on which the direction of motion in the

x

–direction is constant, express the speed

s(t)

without absolute value signs. (c) Compute the total distance traveled by the particle for

0\le t\le 5

seconds. (d) Calculate the magnitude of the particle’s displacement over the same interval and interpret the result in the context of the motion.