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 changes with time as d K / d t = γ t , where γ is a positiv

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 changes with time as d K / d t = γ t , where γ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

TestHub · Accepted Answer

Given the change in kinetic energy d k d t = γ t . Kinetic energy is expressed as k = 1 2 m v 2 . ∴ d k d t = m v d v d t = γ t Integrating the above relation, m ∫ 0 v v d v = γ ∫ 0 t t d t m v 2 2 = γ t 2 2 v = γ m t ; υ ∝ t ... (i) a = d v d t = γ m = c o n s t a n t Since F = m a ∴ F = m γ m = γ m = c o n s t a n t

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