Final answer:
The kinetic energy of a particle of mass m acted upon by a force P for a time t is given by option B, which is P²t²/2m. This is derived from the formula for kinetic energy and Newton's second law of motion.
Step-by-step explanation:
The subject of the question is Physics, and it pertains to the concept of kinetic energy which is related to the mass of a particle and its velocity. The formula for kinetic energy (K.E.) is given by K.E. = 1/2 * m * v², where m represents the mass and v is the velocity of the particle.
According to Newton's second law, force equals the change in momentum (p = mv) over time or the mass times the acceleration (F = ma). Given that the particle starts from rest, its initial velocity is zero. The force applied for a time t will result in an acceleration, which in turn gives the particle its velocity. The velocity is calculated by v = (P/m) * t, where P is the force acting on the particle. Substituting this into the kinetic energy formula gives K.E. = 1/2 * m * ((P/m) * t)² = P² * t² / (2m), which corresponds to option B. P²t²/2m.