A particle moves along a line with position given by s(t)= cases t^ 2 +1, & 0 t 3,…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

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

(b)

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

(c)

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

(d)

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