Let represent the position (in meters) of a particle moving along a horizontal line…

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

s(t)=t^{3}-6t^{2}+9t

represent the position (in meters) of a particle moving along a horizontal line for

0\le t\le 5

seconds. (a) Determine the velocity

v(t)

and acceleration

a(t)

of the particle. (b) Find all times in the interval

0\le t\le 5

at which the particle is at rest, and classify each as a relative minimum or maximum of

s

. Justify your classification. (c) Determine the intervals on

0<t<5

during which the particle is speeding up and the intervals during which it is slowing down. Support your intervals with appropriate sign charts for

v

and

a

. (d) Compute (i) the displacement and (ii) the total distance traveled by the particle over the time interval

0\le t\le 5

. Include units in your answers.