Mathematics

Problem

A particle moves along a line so that its position (in meters) at time

t

seconds is given by

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

. Which of the following statements correctly compares the instantaneous velocity at

t = 4

with the average velocity on the interval

3 \le t \le 5

? a) The instantaneous velocity at

t = 4

10\,\text{m/s}

, which equals the average velocity on

[3,5]

. b) The instantaneous velocity at

t = 4

9\,\text{m/s}

, which is less than the average velocity of

10\,\text{m/s}

[3,5]

. c) The instantaneous velocity at

t = 4

9\,\text{m/s}

, which is greater than the average velocity of

10\,\text{m/s}

[3,5]

. d) The instantaneous velocity at

t = 4

9\,\text{m/s}

, which equals the average velocity of

9\,\text{m/s}

[3,5]