For a particle

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

Problem

For a particle, displacement as a function of time is

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

(in metres). At what time does its velocity first become zero and what is the magnitude of acceleration at that instant? (a)

t=1\,\text{s},\;|a|=6\,\text{m\,s}^{-2}

(b)

t=3\,\text{s},\;|a|=6\,\text{m\,s}^{-2}

(c)

t=1\,\text{s},\;|a|=0\,\text{m\,s}^{-2}

(d)

t=4\,\text{s},\;|a|=12\,\text{m\,s}^{-2}