A particle’s position is given by s(t)= cases 4t-3 & 0 t 2 t^ 2 +1 & t>2 cases

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A particle’s position is given by

s(t)=\begin{cases}4t-3 & 0\le t\le 2\\ t^{2}+1 & t>2\end{cases}.

Explain why equality of the two pieces at

t=2

is necessary for the motion to represent a single uninterrupted trip along a line.