Driver

The car driver drove at 100 km/h saw the obstacle and began braking with a slowing of 5 m/s². What is the pathway's length to stop the car when the driver has registered the obstacle with a delay of 0.7 seconds?

Correct answer:

s =  96.6049 m

Step-by-step explanation:

$$\begin{gathered} v=100\text{km/h}\to \text{m/s}=100:3.6\text{m/s}=27.77778\text{m/s} \\ a=5{\text{m/s}}^2 \\ d=0.7\text{s} \\ {s}_0=v\cdot d=27.7778\cdot 0.7=\frac{175}{9}\doteq 19.4444 \\ t=v/a=27.7778/5=\frac{50}{9}\doteq 5.5556\text{s} \\ {s}_1=\frac{1}{2}\cdot a\cdot t^2=\frac{1}{2}\cdot 5\cdot 5.5556^2=\frac{6250}{81}\doteq 77.1605\text{m} \\ s=s_0+s_1=19.4444+77.1605=96.6049\text{m} \end{gathered}$$

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