A single conservative force acting on a particle varies as F=(-Ax + Bx^2)i N where A and B are constants and?

Question

x is in meters
a) calculate the potential energy U(x) associated with this force taking U=0 at x=0
b)find the change in the potential energy and the change in kinetic energy as the particle moves from cx=2m to x=3m


thanks alot !

Answer 1

F=dU/dx so U=integral {(-Ax + Bx^2)dx} from 0 to x

Answer 2

the flair ability would be saved indoors the particle by using a paintings. F(x) = 20 - 4x enable the particle strikes a small distance dx which corresponds to a small paintings performed on it dW. then dW = F.dx dW = (20 - 4x)dx finished quantity of paintings performed in shifting particle from x = 0 to x = 4 is mandatory indoors limits 0 to 4. Integrating this expression aspects W = 20x - 2x^2 using the obstacles, W = 20(4-0) - 2(4-0)^2 W = 80 - 32 => W = 40 8 J the techniques-blowing answer is d)