Car acceleration time

The car starts with constant acceleration, and at a distance of 567 m, it has a speed of 12.6 m/s. How long will it take from the start?

Final Answer:

t =  90 s

Step-by-step explanation:

$$\begin{gathered} s=567\text{m} \\ v=12.6\text{m/s} \\ v=a\cdot t \\ s=\frac{1}{2}\cdot a\cdot t^2 \\ s=\frac{1}{2}\cdot (v/t)\cdot t^2=v\cdot t/2 \\ t=2\cdot s/v=2\cdot 567/12.6=90=90\text{s} \\ \text{ Verifying Solution: } \\ a=v/t=12.6/90=\frac{7}{50}=0.14{\text{m/s}}^2 \\ {s}_2=\frac{1}{2}\cdot a\cdot t^2=\frac{1}{2}\cdot \frac{7}{50}\cdot 90^2=567\text{m} \\ {v}_2=a\cdot t=\frac{7}{50}\cdot 90=\frac{7\cdot 90}{50}=\frac{630}{50}=\frac{63}{5}=12.6\text{m/s} \end{gathered}$$

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