Mathematics

Problem

An object moves along a straight line with position defined by

p(t)=\begin{cases}3t^{2}-12t+5,&0\le t\le 2,\\-t^{2}+8t-7,&2< t\le 6,\end{cases}

where

p

is measured in meters and

t

in seconds. Determine whether

p(t)

is continuous at

t=2\text{ s}

and state the reason for your conclusion.