A force in the +x-direction with magnitude F(x)=18.0N−(0.530N/m)x is applied to a 8.30 kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box.

Question

A force in the +x-direction with magnitude F(x)=18.0N−(0.530N/m)x is applied to a 8.30 kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only horizontal force on the box.
Part A
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.

bobpursley · Answer

We know that work = ʃ F∙dx = 18x - 0.53x²/2 evaluated from 0 to 16
= 18*16 - 0.53*16²/2 = ......... of work done on the box
Therefore the KE of the box = above work = ½*m*V²
-----> V = sqrt(2* work)