Mathematics

Problem

A particle moves along a straight line with position

s(t)=3t^{3}-15t^{2}+18t

meters for

0\le t\le 4

seconds. Which statement correctly compares the average velocity over the interval

0\le t\le 4

with the instantaneous velocity at

t=2

seconds? a) The average velocity is

6\,\text{m/s}

, and the instantaneous velocity at

t=2

0\,\text{m/s}

; they differ in both magnitude and direction. b) The average velocity is

12\,\text{m/s}

, and the instantaneous velocity at

t=2

-6\,\text{m/s}

; they differ in both magnitude and direction. c) The average velocity is

6\,\text{m/s}

, and the instantaneous velocity at

t=2

-6\,\text{m/s}

; they have equal magnitude but opposite directions. d) The average velocity is

6\,\text{m/s}

, which equals the instantaneous velocity at

t=2

in both magnitude and direction.