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soldi70 [24.7K]
3 years ago
5

A force in the +x-direction with magnitude F(x)=18.0N−(0.530N/m)x is applied to a 8.40 kg box that is sitting on the horizontal,

frictionless surface of a frozen lake. F(x) is the only horizontal force on the box. So, If the box is initially at rest at x=0, what is its speed after it has traveled 16.0 m? Express your answer to three significant figures and include the appropriate units.
Physics
1 answer:
Fynjy0 [20]3 years ago
6 0

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

mv\frac{\mathrm{d} v}{\mathrm{d} x}=F=\left ( 18-0530x\right )dx

\int_{0}^{v}vdv=\int_{0}^{16}\left ( 18-0.530x\right )dx

\frac{mv^2}{2}=\left ( 18x-0530\frac{x^2}{2}\right )_0^{16}

v^2=\frac{288-67.841\times 2}{8.40}

v=7.24 m/s

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