Exercise. Consider the curve shown below, which is traced out by vec$(p)(t).$

If the curve does use arclength as a parameter, what must be true?

$|p^{}{?}^{\text{'}}(t)|$ should be $1$ for all $t.$

$|p^{}{?}^{\text{'}}(t)|$ must be $1$ for some $t>0,$ but not necessarily for all $t.$

${\displaystyle \underset{0}{\overset{t}{}}}|vec(p{)}^{\text{'}}()|d=t$ for all $t.$

${\displaystyle \underset{0}{\overset{t}{}}}|vec(p{)}^{\text{'}}()|d=t$ for some $t>0,$ but not necessarily for all $t.$

$|p^{}(t)|=t$ for all $t.$

$|vec(p)(t)|=t$ for some $t>0,$ but not necessarily for all $t.$