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?

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 = &#947; t , where &#947; is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

Aicharya · Accepted Answer

Given the change in kinetic energy d k d t = &#947; t . Kinetic energy is expressed as k = 1 2 m v 2 . &#8756; &#160; &#160; &#160; d k d t = m v d v d t = &#947; t Integrating the above relation, m &#8747; 0 v v d v = &#947; &#8747; 0 t t d t m v 2 2 = &#947; t 2 2 v = &#947; m t ; &#965; &#8733; t ... (i) a = d v d t = &#947; m = c o n s t a n t Since F = m a &#8756; &#160; &#160; F = m &#947; m = &#947; m = c o n s t a n t

A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along…

Solution