An electrically charged wire on the z axis exerts a force on a proton, which moves on the x axis. The initial conditions for the proton position and velocity are:
x(0) = x0 and v(0) = 0.
The force on the proton is Fx(x) = C /x where C = 3.2×10−15 Nm.
(A) Determine the potential energy function, U(x). Choose x0 to be the reference point; i.e., U(x0) = 0.
(B) Calculate the velocity v at the time when the proton passes the point x = 2 x0.
(C) Calculate the time t when the proton passes the point x = 2 x0. Assume x0 = 1 m.
E= (1/2)m*v^2 + U(x)
The Attempt at a Solution
In part A I integrated F(x) and got U(x)= -C*ln(x)
When I got to part B I tried to find the energy assuming that since U(x0)=0 then KE(v0)=max=E but KE(v0)=0 meaning that energy would have to be zero and the velocity is an imaginary number so I'm lost on what to do. If someone could just point me in the right direction I think I could figure it out from there.