A driver takes 0.20s to apply brakes he sees a need for it . . .

Question : A driver takes 0.20s to apply brakes he sees a need for it. This is called  the reaction time of the driver. If he is driving car at a speed of 54 km/h and the breaks cause a deceleration of 6.0 m/s², find the distance travelled by the car after he sees he need to put the breaks. 

Doubt by Kanan

Solution by Deepesh Sir : 

Here, it should be noted that reaction time is the time when the driver sees the requirement for applying the brakes when the brakes are yet not applied. 

Initial velocity of the car (u) = 54 km/h 
u =54×(5/18) 
u = 15 m/s

Before Applying the brakes, the car is moving with uniform velocity i.e. a'=0 m/s

Reaction time (t') = 0.20 s

Distance covered by the car during this reaction time (s')

Using IInd Equation of Motion
s'=ut'+½a't'
s'=15×0.20+½(0)(0.20)²
s'=3.0+0
s'=3 m

After applying the brakes

Initial velocity of the car (u) = 15 m/s

Final velocity of the car (v) = 0 m/s
acceleration (a) = -6 m/s²

Distance covered by the car after the brakes are applied (s)

Using IIIrd Equation of Motion

v²-u²=2as
(0)²-(15)²=2(-6)s
-225=-12s
225/12 =s
18.75 =s
s=18.75 m 

Total distance travelled by the car after the driver sees the need to put the breaks
= s'+s
= 3.0+18.75
= 21.75 m