We first need to find the work done by the braking force. The work done would be equal to the energy of the lorry. Since the lorry was moving, its energy would be kinetic energy.
So work done by braking force = KE of lorry
Work = ½(mv²)
We know that work done = force x distance
Force x distance = ½(mv²)
Distance = mv² ÷ 2F
Hence, C is correct.