Potential energy of a body of mass 1 ~kg free to move along X -axis is given by U(x)= ( x^2 2 -x ) J . If the total mechanical energy of the body is 2 ~J , then the maximum speed of the body is (Assume only conservative force acts on the body)

Step-by-step solution

Key Idea Total mechanical energy of a system is the addition of potential and kinetic energy E=U+ KE Here, mass of the body, m=1 ~kg , E_ mech =2 ~J So, for U_ = d U(x) d x = d d x [ x^2 2 -x ]=0 aligned & x-1 & =0 & x & =1 aligned Hence, U_ = (1)^2 2 -1=- 1 2 Kinetic energy, KE = 1 2 m v^2= v^2 2 ( m=1 ~kg ) Now, putting the values in above expression, aligned & & 2 & =- 1 2 + v^2 2 & & v^2 & =5 & & v & = 5 ~m / s aligned Hence, the correct option is (a).