The position of a particle is given by (SI units)

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The position of a particle is given by

x(t)=t^{3}-6t^{2}+9t+5

(SI units). Between

t=0\,\text{s}

and

t=3\,\text{s}

, at which one of the following instants does the instantaneous velocity equal the average velocity over the entire interval? (a)

2.0\,\text{s}

(b)

1.0\,\text{s}

(c)

1.5\,\text{s}

(d)

0.5\,\text{s}