Mathematics

Problem

A particle’s position is defined by

s(t)= \begin{cases} t^{2}+1, & t\le 3,\\ 6t-8, & t>3. \end{cases}

Which of the following statements about the particle’s instantaneous velocity at

t=3

seconds is correct? a) The instantaneous velocity exists and equals

10\,\text{units/s}

. b) The instantaneous velocity exists and equals

6\,\text{units/s}

. c) The instantaneous velocity does not exist because the velocities from the left and right differ. d) The instantaneous velocity exists and equals

3\,\text{units/s}