Vehicle acceleration

I have specified that the vehicle has an acceleration of 2 m/s², and I need to find out how many meters it will travel if it reaches 64 km/h and also states how long it takes for the vehicle to travel every one meter.

Final Answer:

x =  79.0123 m

Step-by-step explanation:

$$\begin{gathered} a=2{\text{m/s}}^2 \\ v=64\text{km/h}\to \text{m/s}=64:3.6\text{m/s}=17.77778\text{m/s} \\ v=at \\ t=v/a=17.7778/2=\frac{80}{9}\doteq 8.8889\text{s} \\ x=\frac{1}{2}\cdot a\cdot t^2=\frac{1}{2}\cdot 2\cdot 8.8889^2=\frac{6400}{81}\doteq 79.0123\text{m} \\ \text{ Verifying Solution: } \\ {s}_1=1\text{m} \\ {t}_1=\sqrt{2\cdot s_1/a}=\sqrt{2\cdot 1/2}=1\text{s} \\ {s}_2=2\text{m} \\ {t}_2=\sqrt{2\cdot s_2/a}-t_1=\sqrt{2\cdot 2/2}-1\doteq 0.4142\text{s} \\ {s}_3=3\text{m} \\ {t}_3=\sqrt{2\cdot s_3/a}-t_1-t_2=\sqrt{2\cdot 3/2}-1-0.4142\doteq 0.3178\text{s} \\ {s}_4=4\text{m} \\ {t}_4=\sqrt{2\cdot s_4/a}-t_1-t_2-t_3=\sqrt{2\cdot 4/2}-1-0.4142-0.3178\doteq 0.2679\text{s} \\ {s}_5=5\text{m} \\ {t}_5=\sqrt{2\cdot s_5/a}-t_1-t_2-t_3-t_4=\sqrt{2\cdot 5/2}-1-0.4142-0.3178-0.2679\doteq 0.2361\text{s} \\ {s}_6=6\text{m} \\ {t}_6=\sqrt{2\cdot s_6/a}-t_1-t_2-t_3-t_4-t_5=\sqrt{2\cdot 6/2}-1-0.4142-0.3178-0.2679-0.2361\doteq 0.2134\text{s} \end{gathered}$$

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