Kinematics: force along x-axis problem

[vsage]

The only force acting on a 2.7 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 at x = 4?

I found it to be 0.22m/s but my friends swear up and down it's not. Could I get a second opinion on this answer? My work is something like this:

F = -6x
a = -6/2.7 * x
v = -3/2.7 * x^2 +c

v(3) = 8

8 = -3/2.7 * 3^2 + c
c = 18

v(4) = -3/2.7 * 4^2 + 18
v(4) = 0.222

Corrections please? Thanks in advance.

 

[stunner5000pt]

W = d(Kinetic energy) = (Integral from inital to final ) F dx

that's what you're missing

 

[vsage]

heh that makes sense. I had forgotten the point of the entire homework assignment I was helping with was work-related. I still can't figure out why my way didn't work though oh well.

 

[stunner5000pt]

It didn't work BECAUSE!

F = -6x
a = -6/2.7 * x
v = -3/2.7 * x^2 +c

First of all what are you thinking about here how did you figure (ASSUME) that a = 6 / 2.7 x
and how did you derive v from that ?

v(3) = 8

8 = -3/2.7 * 3^2 + c
c = 18

v(4) = -3/2.7 * 4^2 + 18
v(4) = 0.222

Seems you tried to find the difference betwee nthe two points on force

Remember that is W is the integral because it is the area under the graph of force and the only way to do that is to find the integral