A particle of mass m moves on the x -axis as follows: It starts from rest at t = 0 from…

Physics · JEE Advanced · NTA Exams — Kinematics

A particle of mass m moves on the x-axis as follows: It starts from rest at t = 0 from the point x = 0, and comes to rest at t = 1 at the point x = 1 . No other information is available about its motion at intermediate times
(0 < t < 1). If a denotes the instantaneous acceleration of the particle, then:
  1. a cannot remain positive for all t in the interval
    0 ≤ t ≤ 1
  2. |a| cannot exceed 2 at any point in its path.
  3. |a| must be ≥ 4 at some point or points in its path.
  4. a must change sign during the motion, but no other assertion can be made with the information given.

Answer

(C) | a | must be ≥ 4 at some point or points in its path.

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