The velocity of a particle moving along the -axis is given by v(t)=3t^ 2 -6t+4 where…

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The velocity of a particle moving along the

x

-axis is given by

v(t)=3t^{2}-6t+4

where

v

is in

\text{m\,s}^{-1}

and

t

in seconds. The particle passes through the origin at

t=0\,\text{s}

. (a) Find the expression for its acceleration as a function of time. (b) Calculate the displacement of the particle between

t=0\,\text{s}

and

t=3\,\text{s}

. (c) Determine the average velocity of the particle for the interval

0\,\text{s}\le t\le3\,\text{s}