The only force acting on a 2.3 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.
At what positive value of x will the body have a velocity of 5.0 m/s?
I'm not sure how to approach this. So far I have written down KE=(1/2)mv^2,
but I haven't the slightest idea where to go from here...

Question

The only force acting on a 2.3 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. 
At what positive value of x will the body have a velocity of 5.0 m/s? 
I'm not sure how to approach this. So far I have written down KE=(1/2)mv^2, 
but I haven't the slightest idea where to go from here...

anonymous · Answer

$$F = ma$$
-6x = (2.3)a
-60x/23 = a

$$Vf^2 = Vo^2 + 2ad$$
5^2 = 8^2 + 2(3)a
25 = 64 + 6a
-39 = 6a
-13/2 = a

-60x/23 = -13/2
-60x = -299/2
-120x = -299
x = 2.49
(I think. I just kind of made this up and have never dealt with a problem like this before, but I think this might be the answer, and I'd be pleasantly surprised to find out so.)