A body of mass 1 kg moves along a straight line with a velocity v = 2x^2 . The work done by the body during displacement from x = 0 to 5 m is __________ J.

Step-by-step solution

Given mass m = 1 kg and velocity v = 2x^2 . According to the work-energy theorem, the work done by the net force is equal to the change in kinetic energy of the body. W = K = K_f - K_i At x = 0 m, initial velocity v_i = 2(0)^2 = 0 m/s. At x = 5 m, final velocity v_f = 2(5)^2 = 50 m/s. Initial kinetic energy K_i = 1 2 m v_i^2 = 0 J. Final kinetic energy K_f = 1 2 m v_f^2 = 1 2 1 (50)^2 = 1250 J. Work done W = 1250 - 0 = 1250 J. Answer: 1250