1. In a cheese-rolling competition, a cylindrical block of cheese is rolled down a hill, and then continues to roll along a horizontal surface.

Its acceleration, $am{s}^{-2}$ , is modelled by the functions

 a(t)=\{\begin{matrix}0.2t0\leqt\leq15\\9-t15</p><p style="line-height: 1.7" class="text-lg tracking-wide font-normal leading-relaxed">where \(t is the time in seconds and $A$ is a constant.

The block of cheese comes to rest when its acceleration is $−9m{s}^{-2}.$

Find the distance the block of cheese rolls before it comes to rest.