What is the total energy of the body at x=4 meters?

[sciencegeek26]

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.

What is the velocity of the body at x=4?

At what positive value of x will the body have a velocity of 5 m/s?

I got the answer to the second question just fine, which ended up being 5.3. I feel like I just am doing the first one wrong. What is the proper equation for it? I thought it would be
-6/2(4^2-3^2). Or at least that is what my teacher said would give me the correct answer. Alas that is not so. I just need the proper way to do the first one now.

 

[Doc Al]

What's the total energy of the body at x = 3 and at x = 4? Set up an equation and then you can solve for the speed.

 

[sciencegeek26]

I got it to be -21J but I think I'm using the wrong equation

 

[Doc Al]

I got it to be -21J but I think I'm using the wrong equation

What equation are you using?

 

[sciencegeek26]

What equation are you using?

(1/2)m(v2^2-3^2)

Instead of 3 being squared should it be 8m/s? Then I would get -69.6J

 

[Doc Al]

(1/2)m(v2^2-3^2)

Instead of 3 being squared should it be 8m/s? Then I would get -69.6J

You need to fix that formula. The total energy is the sum of the kinetic energy and the spring potential energy. How would you express spring potential energy?