A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the $$x-axis$$. Its kinetic energy K changes with time as $$dKdt=$$γt, where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

Question

A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the $$x-axis$$. Its kinetic energy K changes with time as  $$dKdt=$$γt, where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

Infinity Learn · Accepted Answer

$$dKdt=yt$$ as $$K=12mv2$$∴$$dKdt=mvdvdt=yt$$∴m∫$$0v$$ $$vdv=y$$∫$$0t$$ tdt⇒$$mv22=yt22$$⇒$$v=ymt$$⇒$$a=dvdt=ym=$$ Constant  and $$S=12at2=12ymt2$$ Since $$F=ma$$∴$$F=mym=ym=$$ Constant Since force applied is constant, it is conservative in nature.

A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as $\frac{d K}{d t} = γ t$ , where $γ$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

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A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as dKdt=γt, where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

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A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as $\frac{d K}{d t} = γ t$ , where $γ$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?