posted by Anonymous .
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...
What you have is a spring-mass system, with spring constant 6.0 N/m.
Total energy, which is constant, is
(1/2)kX^2 + (1/2)MV^2
= 3*9 + 1.15*64 = 100.6 J
(using data at the X = 3.0 m location)
Solve for X when V = 5 m/s
100.6 = 3*X*2 + 1.15*25
X^2 = 23.95 m^2
X = 4.9 m