Question

A force in the +x-direction with magnitude F(x)=18.0N−(0.530N/m)x is applied to a 8.70kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box.

If the box is initially at rest at x=0, what is its speed after it has traveled 12.0m ?

Answer 1

Take the integral of F(x) which is

18.0x-.5(.530)x^2 then plug in 12.0 for x
=177.84J
so .5mv^2=W since v(initial) is zero so then solve for v
v(final)=((2*177.84)/8.7)^(1/2)
v(final)=6.39m/s