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 dK/dt= t, where is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

JEE Advanced 2018 Physics question

Physics Motion in a Straight Line JEE Advanced 2018

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

(A)The force applied on the particle is constantCorrect
(B)The speed of the particle is proportional to timeCorrect
(C)The distance of the particle from the origin increases linearly with time
(D)The force is conservativeCorrect

Answer: (A),(B),(D)

Solution

Integrating, : the speed is proportional to time, (B) true. Then is constant, so the force is

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Question ID VK-026754