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.
Speed of car $=54 \times \frac{5}{18}=15 \mathrm{~m} / \mathrm{s}$
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
$\mathrm{u}=15 \mathrm{~m} / \mathrm{s} ; \mathrm{a}=-6 \mathrm{~m} / \mathrm{s}^{2} ; \mathrm{v}=0 \mathrm{~m} / \mathrm{s}$
$\mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}$
$0^{2}=(15)^{2}+2(-6) \mathrm{S}_{2}$
$\mathrm{S}_{2}=18.75 \mathrm{~m}$
Total distance $=\mathrm{S}_{1}+\mathrm{S}_{2}$
$=3+18.75$
$=21.75 \mathrm{~m}$
$\approx 22 \mathrm{~m}$
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