</span><span><span>Ff</span>=<span>Uk</span>mg=0.45m(9.8m/<span>s2</span>)</span> Calculate the acceleration (which will be negative since it's due to the force of friction):
<span> a=<span>Fm</span></span><span>a=<span><span>(0.45)(9.8m/<span>s2</span>)m</span>m</span></span><span>a=4.41m/<span>s2</span></span>
Time to stop:<span>t=<span><span>8.55m/s</span><span>4.41m/<span>s2</span></span></span>=1.94s</span>
Now see how far they go in 1.94s with an acceleration of -4.41m/s^2:<span>x=<span>V0</span>t+<span>12</span>a<span>t2</span></span><span>x=(8.55m/s)(1.94s)+<span>12</span>(−4.41m/<span>s2</span>)(1.94s<span>)2</span>=8.29m</span>
Seeing the graph from desmos.com, we know there is only one place where the graph will go up then down, or down then up given that the maximum exponent of x is it squared. That place, as seen, is -0.375 for the minimum as it goes down then up. There's no maximum in sight :(
