For what value of x will this object first come to rest?

[gijungkim]

Homework Statement

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?

Homework Equations

0.5 mv^2 = KE
F*d = work

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?

 

[AdityaDev]

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 can't find the net work done like this:

and F*d = -4.0x^2

everything else is correct. Just the left hand side of the equation.

 

[gijungkim]

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 can't find the net work done like this:

everything else is correct. Just the left hand side of the equation.

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!

 

[AdityaDev]

The force changes as the position of particle changes. So you can't get the value of work done by simply multiplying F with x.

 

[gijungkim]

The force changes as the position of particle changes. So you can't get the value of work done by simply multiplying F with x.

Got it now! Thank you for helping me!