Physics Please help !!
posted by member of physics .
A single conservative force = (6.0x  12) N where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 23 J at x = 0.
(a) Write an expression for U as a function of x, with U in joules and x in meters.
U(x) =
(b) What is the maximum positive potential energy?
J
(c) At what negative value of x is the potential energy equal to zero?
m
(d) At what positive value of x is the potential energy equal to zero?
m

ΔU = U(x)  U(0) = ∫(6x  12)dx
Therefore, with U(0) = 23 J, we obtain by integrating
U = 23 + 12x  3x ²
F = 0 when 6x  12 = 0
Thus x = 2 m
Substituting into U = 23 + 12x²  3x ,
U = 35 J
Using the quadratic equation find the negative and positive values of x for which U = 0
3x ²  12x23 =0
x=(12±sqrt(144+4•3•23)}/2•6
x = 1.42 m
x = 5.42 m