The correct option is A 2 J
Given,
Potential energy function of the particle
U=x2−3x ......(1)
Since, U is function of position only, we call the force associated with this potential as conservative force.
General relation between a conservative force and potential energy is given by
→F=−(∂U∂x^i+∂U∂y^j+∂U∂z^k)
From (1) we can deduce that, U is a function of x only.
∴ The above formula can be written as,
F=−dUdx
⇒F=−2x+3 .......(2)
Since, the force is a variable force, From Newton's second law we can write that,
F=ma=mdvdt=mdvdx.dxdt
⇒F=mvdvdx .........(3)
From (2) and (3)
mvdvdx=−2x+3
Integrating,
m∫v0vdv=∫x0(−2x+3)dx
⇒mv22=K.E=−x2+3x
∴(K.E)x=2=−22+6=2 J
Thus, option (a) is the correct answer.