An object of mass $$2$$ kg is placed at rest on a frictionless horizontal surface. A horizontal force is given by F¯ $$=$$ (x2$$−$$9)ℓ∧ N acts on it along $$x-axis$$. Kinetic energy of the object will be maximum at

Question

An object of mass $$2$$ kg is placed at rest on  a frictionless horizontal surface.  A horizontal force is given by F¯  $$=$$    (x2$$−$$9)ℓ∧ N  acts on it along $$x-axis$$.  Kinetic energy of the object will be maximum at

Infinity Learn · Accepted Answer

from work energy theorem work done $$=$$ change in $$KE$$ $$d($$$$KE$$$$)=dW=$$ F.dx ⇒$$KE$$$$=$$∫ F.dx $$KE$$ $$=$$    ∫(x2$$−$$9) dx  $$=$$   $$x33$$−$$9x$$ to find $$KE$$ is maximum or minimum , $$ddxKE=0$$ ⇒$$(x2$$−$$9)=0$$ ⇒$$x=$$±$$3$$ case $$1$$: if x $$=+3$$ →$$d2dx2KE=ddx(x2$$−$$9)=2x=2(3)=+6$$ is positive⇒minimum case $$2$$: if x $$=-3$$ →$$d2dx2KE=2(-3)=-6$$ is negative⇒maximum ∴$$KE$$ is maximum at $$x=-3m$$

An object of mass 2 kg is placed at rest on a frictionless horizontal surface. A horizontal force is given by $\bar{F} = (x^{2} - 9) \overset{\land}{ℓ} N$ acts on it along x-axis. Kinetic energy of the object will be maximum at

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An object of mass 2 kg is placed at rest on a frictionless horizontal surface. A horizontal force is given by F¯ = (x2−9)ℓ∧ N acts on it along x-axis. Kinetic energy of the object will be maximum at

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An object of mass 2 kg is placed at rest on a frictionless horizontal surface. A horizontal force is given by $\bar{F} = (x^{2} - 9) \overset{\land}{ℓ} N$ acts on it along x-axis. Kinetic energy of the object will be maximum at