A particle moves according to:

x$($t$)=$rcos$($ct$)$

y$($t$)=$rsin$($ct$)$

where r$=1$m and c$=5$ra$($d$)/($s$).$

$($a$)$ Show that the speed of the particle is constant.

$($b$)$ How much time does the particle take to go from P at $(0,1$m$)$ to Q at $(1$m$,0)$

$?$

$($c$)$ What is the acceleration of the particle at point Q $?$