Why Is the Force Acting on the Object -3k When x=0?

[UrbanXrisis]

The potential energy of an object is given by U(x)=0.5kx^2+3kx, where U is joules, x is in meters and k is a constant. What is the force acting on the object when x=0?

PE=Fd
0.5kx^2+3kx=Fd
0.5kx+3k=F
F=3k

The answer is -3k, why?

 

[Nothing]

Recall Work = -(delta)PE

Fd = -(0.5kx^2 + 3kx)
F = -0.5kx - 3k
F = -3k , x = 0

 

[UrbanXrisis]

what is work for KE?

W=.5mv^2
or
W=-.5mv^2

 

[Doc Al]

The relationship between the potential function and the force is this: F = - dU/dx.

 

[UrbanXrisis]

would the object's Kinetic energy be positive then?

 

[Doc Al]

would the object's Kinetic energy be positive then?

Beats me. That depends on the total mechanical energy, which you have not specified.