# Homework Help: For what value of x will this object first come to rest?

1. Mar 23, 2015

### gijungkim

1. The problem statement, all variables and given/known data
A 2.0-kg body moving along the x axis has a velocity vx = 5.0 m/s at x = 0. The only force acting on the object is given by Fx = (–4.0x) N, where x is in m. For what value of x will this object first come (momentarily) to rest?

2. Relevant equations
0.5 mv^2 = KE
F*d = work

3. The attempt at a solution
Since KE = 0.5 * 2 * 5^2 = 25J
and F*d = -4.0x^2
-4x^2 = 25J
x = 2.5 m
This is how I approached it, but the answer is 3.5m. Can anyone help me out?

2. Mar 23, 2015

Since the force changes with x, what will be the work done by the force when the body moves by a distance dx?
Integrate it to find the total work and the expression you get comes out to be different. why?
you cant find the net work done like this:
everything else is correct. Just the left hand side of the equation.

3. Mar 23, 2015

### gijungkim

Oh I got it now
Fxdx = -4.0x dx
W = -2.0x^2 J = 0.5 * 2 * 5^2 J
x = 3.5m right??
Thank you so much!

4. Mar 23, 2015