An electron starting from rest and moving with the velocity v through a potential difference V is shown by the graphs below. Identify the correct graph.

Step-by-step solution

The kinetic energy gained by an electron of mass m and charge e when accelerated through a potential difference V is given by the work-energy theorem as K = eV . The kinetic energy is also expressed as K = 1 2 mv^2 , where v is the velocity of the electron. Equating the two expressions, we have 1 2 mv^2 = eV . Solving for velocity v , we get v^2 = 2eV m , which implies v = 2e m V . This equation is of the form v = k V , where k = 2e m is a constant. The relationship between v and V is a parabolic curve where v incr