A particle is moving along the $x-$axis so that its velocity at any time $t$ is given by $v(t)=6t-t^2.$ Which of the following statements is$/$are correct.

I. The particle is moving to the right when $t=5.$

II$.$ If $p(t)$ were the position function for the particle, then the total distance on the interval $|p(1)-p(5)|t=51$ would $be|p(1)-p(5)|.$

III. $Att=5,$ the speed $of$ the particle $is$ increasing.

$A.$ I and III only

$B.II$ only

$C.$ I and $II$ only

$D.$ I, $II,$ and III