Mathematics

Problem

A particle moves along a line with position given by

s(t)=\begin{cases} t^{2}+1, & 0\le t\le 3,\\[2pt] at+b, & 3<t\le 5. \end{cases}

Which of the following conditions must be satisfied to ensure the particle does not experience an instantaneous jump in position at

t=3

? a)

a=6

\displaystyle \frac{d}{dt}\bigl(t^{2}+1\bigr)\Big|_{t=3}=\frac{d}{dt}(at+b)\Big|_{t=3}

t^{2}+1\big|_{t=3}=at+b\big|_{t=3}

t^{2}+1\big|_{t=3}=\dfrac{d}{dt}(at+b)\big|_{t=3}