Answer:
Initial speed Vo=631.229 mi/h
Explanation:
For this problem, I used miles instead of meters, because that seems more accurate. Since the final speed is 10% (0.1) higher than initial, then mathematically it means
[tex]V_{f}=V_{o}+0.1*V_{o}=1.1*V_{o}[/tex]
First, find the acceleration, with this formula
[tex]V^{2} _{f}-V^{2}_{o}=2*a*dist[/tex]
Which results in
[tex]a=\frac{(1.1*V _{o})^{2}-V^{2}_{o}}{2*57000} =0.000002*V_{o}^{2}[/tex]
Now substitute in this equation:
[tex]V _{f}-V_{o}=a*t\\ (1.1-1)*V_{o}=0.000002*V_{o}^{2}*86[/tex]
This became in a quadratic equation. Dividing both sides by initial speed and solving and, since we used time in Hours and for distance miles, then the speed should have units of miles per hour:
[tex]0.1*V_{o}=0.000158*V_{o}x^{2} \\ V_{o}=631.229mi/h[/tex]
