Answer:v=7.24 m/s
Explanation:
Given
F(x)=18-0.530 x
mass m=8.40 kg
box is at rest at x=0
Distance traveled=16 m
[tex]mv\frac{\mathrm{d} v}{\mathrm{d} x}=F=\left ( 18-0530x\right )dx[/tex]
[tex]\int_{0}^{v}vdv=\int_{0}^{16}\left ( 18-0.530x\right )dx[/tex]
[tex]\frac{mv^2}{2}=\left ( 18x-0530\frac{x^2}{2}\right )_0^{16}[/tex]
[tex]v^2=\frac{288-67.841\times 2}{8.40}[/tex]
[tex]v=7.24 m/s[/tex]
