A particle moves along a straight line with its position given by (in metres) for

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

Problem

A particle moves along a straight line with its position given by

x(t)=10t^{2}-4t^{3}

(in metres) for

0\le t\le4\,\text{s}

. During this interval, at what time

t

does the magnitude of its instantaneous velocity equal the magnitude of its average velocity between

t=0

and

t=4\,\text{s}

? (a)

1.25\,\text{s}

(b)

3.2\,\text{s}

(c)

2.5\,\text{s}

(d)

0.83\,\text{s}