We know that force ( F ) is directly proportional to acceleration (a) by Newton's second law ( F=ma ). Therefore, if the force is always perpendicular to the velocity, then the acceleration is also always perpendicular to the velocity. The work done by a force is given by W=∫F⋅ds, where ds is the displacement. Since, F is perpendicular to v and ds is in the direction of v, the dot product F⋅ds=0. This means the work done by the force is zero. According to the work-energy theorem, the net work done on a particle equals the change in its kinetic energy ( ∆KE ). Since the work done is zero, the change in kinetic energy is zero, meaning the kinetic energy remains constant.