A particle starts moving from time t = 0 and its coordinate is given as x(t) = 4t³ - 3t. (A) The particle returns to its original position (origin) 0.866 units later. (B) The particle is 1 unit away from origin at its turning point. (C) Acceleration of the particle is non-negative. (D) The particle…

Question

A particle starts moving from time t = 0 and its coordinate is given as x(t) = 4t³ - 3t. (A) The particle returns to its original position (origin) 0.866 units later. (B) The particle is 1 unit away from origin at its turning point. (C) Acceleration of the particle is non-negative. (D) The particle is 0.5 units away from origin at its turning point. (E) Particle never turns back as acceleration is non-negative. Choose the correct answer from the options given below:

Accepted Answer

(1) A, B, C only. Return to origin: 4t³ - 3t = 0 ⇒ t² = 3/4 ⇒ t = 0.866. Statement A is true. Velocity: v = 12t² - 3 = 0 ⇒ t = 0.5, the turning point. x(0.5) = 4(0.125) - 1.5 = -1, so the particle is 1 unit from the origin there. B is true, D is false. Acceleration: (dv)/(dt) = 24t ≥ 0 for t ≥ 0. C is true. The particle starts with v = -3, stops at t = 0.5 and comes back, so it does turn back: E is false. A, B and C only.

Step-by-step solution

Why the other options are wrong