Question $4(15$ pts$.)$: A driver travelled on a road with a $-3\%$ grade and struck a workzone flagger $($the person who holds the stop or slow$-$down sign at workzones$).$ The posted speed limit on this road is $45m\frac{i}{h}r.$ The accident investigation team determined the following: the driver saw the flagger at $500$ feet, the driver did not apply his brakes until he was $200$ feet away from the flagger, and the driver struck the flagger at $20m\frac{i}{h}r.$ Explain why the driver was at fault. Your explanation should address both his speed and reaction time.