A particle moves along an x axis. Does the kinetic energy of the particle increase, decrease, or remain the same if the particle’s velocity changes (a) from −3 m/s to −2 m/s and (b) from −2 m/s to 2 m/s? (c) In each situation,isthe work done on the particle positive,negative,or zero?

(a) The kinetic energy of a particle is given by the formula KE = 1/2 mv^2, where m is the mass of the particle and v is its velocity. The kinetic energy depends on the square of the velocity, so it doesn't matter if the velocity is positive or negative. When the velocity changes from -3 m/s to -2 m/s, the magnitude of the velocity decreases. However, since the kinetic energy depends on the square of the velocity, the kinetic energy actually increases.

(b) When the velocity changes from -2 m/s to 2 m/s, the magnitude of the velocity remains the same. Therefore, the kinetic energy of the particle remains the same.

(c) The work done on a particle is given by the formula W = Fd, where F is the force applied on the particle and d is the displacement of the particle. If the force is applied in the direction of the displacement, the work done is positive. If the force is applied in the opposite direction of the displacement, the work done is negative. If the force is perpendicular to the displacement, the work done is zero. In this case, since the velocity (and therefore the displacement) of the particle is changing, the work done on the particle is positive in the first case (as the kinetic energy increases) and zero in the second case (as the kinetic energy remains the same).