A driver takes 0.20 s to apply the brake after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of 54 km/h and the brakes cause a deceleration of 6 m/$s^2$ find the distance traveled by car after he sees the need to put the brakes on.

Step 1, Given

Reaction time = 0.20 sec

Speed = 54 km/h = 15 m/s

Step 2, Finding the distance traveled

In reaction time, the body moves with speed of 54 km/h = 15 m/s (constant speed).

Distance traveled in this time,

$S_1=1.5\times 2=3m$

When brakes are applied,
$\text{u = 15 m/s}$
$\text{v = 0}$
a = - 6 m/$s^2$ (deceleration)

From the third equation of motion

We know, $S_2=\frac{v^2-u^2}{2a}$
Or, putting all the values

$S_2=\frac{0^2-{15}^2}{2(-6)}=18.75m$

Total distance = $S_1+S_2=3+18.75=21.75m$
Hence the total distance traveled is 22 m