An object is moving at constant speed around a horizontal circle of radius r$.$ At a particular instant of time t$1,$ the acceleration

a$1=(6\mathrm{.}003\mathrm{.}00)$ m$/$s$2,$

and at a later time t$2,$ the acceleration

a$2=(3\mathrm{.}006\mathrm{.}00)$ m$/$s$2.$

Here, t$1=5\mathrm{.}00$ s and t$2=8\mathrm{.}00$ s$.$ Note that the path of the object is in the x$-$z plane. We use a coordinate system with the $+$x axis to the right, $+$z axis vertically down, and $+$y axis coming toward you.

$($a$)$ What is the period of rotation of the particle if it is moving in the clockwise direction?

s

$($b$)$ What is the period of rotation of the particle if it is moving in the counterclockwise direction?

s

$($c$)$ Find the radius of the path for the two cases indicated in parts $($a$)$ and $($b$).$

clockwise$$ mcounterclockwise$$ m