Question

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.

Answer 1

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

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

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

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

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

$v=7.24 m/s$