A 040kg cart with charge 45 x 105 C starts at rest on a hori

A 0.40-kg cart with charge 4.5 x 10^-5 C starts at rest on a horizontal frictionless surface 0.4 m from a fixed object with charge +2.0 x 10^-1 C. When the cart is released, it moves away from the fixed object. How fast is the cart moving when it is very far (infinity) from the fixed charge? How fast is the cart moving when it is 2.0 m from the fixed object?

Solution

initial E = PE = kQq / d

PE = 8.99e9N·m²/C² * 0.2e-5C * 0.45e-4C / 0.4m = 2.0227 J

At infinite distance, E = KE = 2.0227 J = ½mv² = ½ * 0.40kg * v²

v = 3.180 m/s

B:

At 2.0 m, PE = 8.99e9N·m²/C² * 0.45e-4C * 2e-4C / 2.0m = 0.404 J

so the remaining KE = E - PE = 2.0227 J - 0.404 J = 91.91 J = ½ * 0.40kg * v²

v = 2.84 m/s