Solving for Velocity of a Body with Fx=-6xN

[themanofosu]

Here is the question:

The only force acting on a 2.9 kg body as it moves along the positive x-axis has an x component Fx = - 6x N, where x is in meters. The velocity of the body at x = 3.0 m is 8.0 m/s.

a)What is the velocity of the body at x = 4.0 m?

and

b) At what positive value of x will the body have a velocity of 5.0 m/s?

It does provide a hint : "Work is equal to the change in the kinetic energy. How does work by a spring force depend on the position? What is the value of the spring constant here?"

So I am thinking that K= 6. And that work of the spring = (1/2)(k)(x_initial)^2 - (1/2)(k)(x_final)^2, and we can plug that in for work = (1/2)(m)(v_final)^2 - (1/2) (m)(v_inital)^2 to find the velocity when x = 4. so where did I go wrong here, how do i properly solve this?

 

[tiny-tim]

Hi themanofosu!

Your method looks correct.

But (as with your other thread) it will help in future if you actually show you full calculations …

most members posting about wrong answers turn out to have made a simple arithmetic error.