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The average time taken by a normal person to react to an emergency is one$-$fifteenth of a second and is called the 'reaction time'. If a bus is moving with a velocity of $60\, km h^{-1}$ and its driver sees a child running across the road, how much distance would. the bus had moved before he could press the brakes ? The reaction time of the people increases when they are intoxicated. How much distance had the bus moved if the reaction time of the driver were $\frac{1}{2}\, s$ under the influence of alcohol ?
Solution
Given Speed of the bus $=60 \,km h ^{-1}$
$=\frac{5}{18} \times 60=16.7 m s ^{-1}$
Time of reaction $=\frac{1}{15} s$
Time of reaction under the influence of alcohol $=\frac{1}{2} s$
$(i)$ Distance travelled by the bus in the first case,
distance $=$ speed $\times$ time $=16.7 \times \frac{1}{15}=1.11 m$
$(ii)$ Distance travelled by the bus in the second case,
distance $=$ speed $\times$ time $=16.7 \times \frac{1}{2}=8.35 m$
