Solve the following :
Question:

A driver takes $0.20$ s to apply the brakes 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 $54 \mathrm{~km} / \mathrm{h}$ and the brakes cause a deceleration of $6.0 \mathrm{~m} / \mathrm{s}^{2}$, find the distance travelled by the car after he sees the need to put the brakes on.

Solution:

Speed of car $=54 \times 18=15 \mathrm{~m} / \mathrm{s}$

Distance travelled during reaction time

$\mathrm{S}_{1}=\mathrm{v}^{\mathrm{X}} \mathrm{t}$

$=15 \times 0.2=3 \mathrm{~m}$

When brakes are applied

$\mathrm{u}=15 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-6 \mathrm{~m} / \mathrm{s}^{2} ; \mathrm{v}=0 \mathrm{~m} / \mathrm{s}$

$v^{2}=u^{2}+2 a s$

$0^{2}=(15)^{2}+2(-6) S_{2}$

$\mathrm{S}_{2}=18.75 \mathrm{~m}$

Total distance $=\mathrm{S}_{1}+\mathrm{S}_{2}$

$=3+18.75$

$=21.75 \mathrm{~m}$

$\approx 22 \mathrm{~m}$