- #1
odie5533
- 58
- 0
Homework Statement
A 7.0-kg rock is subject to a variable force given by the equation
[tex]F(x) = 6.0N - (2.0N/m)x + (6.0N/m^2)x^2[/tex]
If the rock initially is at rest at the origin, find its speed when it has moved 9.0m.
The Attempt at a Solution
[tex]\sum F_{x} = 6 - 2x + 6x^2[/tex]
[tex]ma=6 - 2x + 6x^2[/tex]
[tex]a = \frac{6}{7} - \frac{2}{7}x + \frac{6}{7}x^2[/tex]
[tex]V_{f}^2 = V_{i}^2 + 2*a*x[/tex]
[tex]V_{f}^2 = 0 + 2(\frac{6}{7} - \frac{2}{7}x + \frac{6}{7}x^2)x[/tex]
[tex]V_{f}^2 = 2(\frac{6}{7} - \frac{2}{7}(9) + \frac{6}{7}(9)^2)(9)[/tex]
[tex]V_{f} = 1219m/s[/tex]
That seems waaay too fast, and I think I should have used an integral/derivative somewhere since the force changes as x changes. I'm rather lost on this one.