A particle moves along a path $r(t)$ for $0tT,$ beginning at the origin. The vector

$v=\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{}}}{r}^{\text{'}}(t)dt$

is the average velocity vector.

$($a$)$ If $v=0$ where will the particle be located at time $T?$

$($b$)$ If $v=0$ does that moss the awerage speed is necossarily equal to zero?

$($c$)$ Find the average velocity of a particle if $r(t)=(cost,sint,t)$ for $T=1.$