The potential energy of a particle is determined by the expression U $$=$$ a (x2+y2), where α is a positive constant. The particle begins to move from a point with coordinates (3$$,$$3), only under the action of potential field force. Then its kinetic energy T at the instant when the particle is at a point with the coordinates (1$$, $$1) is

Question

The potential energy of a particle is determined by the expression U $$=$$ a (x2+y2), where α is a positive constant. The particle begins to move from a point with coordinates (3$$,$$3), only under the action of potential field force. Then its kinetic energy T at the instant when the particle is at a point with the coordinates (1$$, $$1) is

Infinity Learn · Accepted Answer

As the particle moves only under the action of conservative force, its mechanical energy must be $$conserve(d)$$ So∆T $$+$$ ∆U $$=$$ $$0$$ (T$$ stands for kinetic $$energy)or$$ ∆T $$=$$ $$-$$∆U $$=$$ Ui $$-$$ $$Uf=$$α$$(32$$ $$+$$ $$32) $$-$$α(12$$ $$+$$ $$12) $$=$$ $$16$$α

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