If a car has a maximum deceleration of 7$7$ m/$/$s²,$2,$ the driver's reaction time to apply the brakes is 0.5$0\mathrm{.}5$ seconds and the car must stop in a maximum of 4$4$ m:

 a.$.$ What maximum velocity can the car reach?

b.$.$ What fraction of the braking distance corresponds to the reaction time?