Question

the potential energy of a particle of mass 1 kg moving along x axis is given by U(x) = (x^2/2 - x) J if the total mechanical energy of particle is 2 J then find its maximum speed

Answer 1

2Speed will be max when kinetic energy is maximum so potential energy will be minimum so differentiating the function put it equal to 0 so we obtain minimum for x=0 now kin potential energy is 0 and kinetic energy will be 2 .mv^2/2 is equal to 2 m is 1 kg therefore v=2 .