Mathematics

Problem

For a particle with position

s(t)=t^{2}+2t

metres, answer the following. a. (i) Calculate the average velocity on the interval

t=1\text{ s}

t=3\text{ s}

. b. (ii) Determine the instantaneous velocity at

t=2\text{ s}

. c. (iii) State, with reason, whether the average velocity on

[1,3]

equals the instantaneous velocity at the midpoint of the interval.