man of mass m is stationary on a flat car. the car move without friction along horizontal rails. the man starts walking with velocity v relative to the car

Question

A man of mass m is stationary on a stationary flat car. The car can move without friction along horizontal rails. The man starts walking with velocity v relative to the car. Work done by him is

Answer 1

The work is defined by the difference in kinetic energy of a moving object:

 

W_net = 1/2 mv_f² - 1/2 mv_i² = KE_f - KE_i

 

The man is stationary and his initial velocity v_i was the velocity of the car call it v_car = v_i but the car is also stationary, and  v_car= v_i = 0 in this case . The problem statement does not say that car moved, but the statement says the car can move without friction. the man started moving with relative velocity v, and that is the final velocity v_f. The work done by him is:

 

W_net = 1/2 mv_f² - 1/2 mv_i² = 1/2 mv_f² - 0 = 1/2 mvf² = 1/2mv²