For a particle moving in a straight line

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

Problem

For a particle moving in a straight line, the velocity for

0 \le t \le 5\,\text{s}

is given by

v(t)=\begin{cases}2t^{2}, & 0 \le t \le 3\,\text{s}\\18 - 6t, & 3 < t \le 5\,\text{s}\end{cases}

What is the instantaneous acceleration just after

t = 3\,\text{s}

? (a)

12\,\text{m s}^{-2}

(b)

6\,\text{m s}^{-2}

(c)

-6\,\text{m s}^{-2}

(d)

-12\,\text{m s}^{-2}