A particle starts moving from time t=0 and its coordinate is given as x(t)=4 t³-3 t 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 a

Step-by-step solution

Given x(t) = 4t^3 - 3t , we find v(t) = 12t^2 - 3 and a(t) = 24t . Statement A: Setting x(t) = 0 gives 4t^3 - 3t = 0 t(4t^2-3) = 0 , so t = 0 or t = 3/4 = 0.866 . The particle returns to origin at t = 0.866 units. TRUE. Statement B: Turning points occur at v(t) = 0 12t^2 - 3 = 0 t = 0.5 . At t = 0.5 : x = 4(0.125) - 1.5 = -1 ; distance = 1 unit. At t = -0.5 : x = 1 ; distance = 1 unit. TRUE. Statement C: For t 0 (particle starts at t=0 ), a(t) = 24t 0 . TRUE. Statement D: At turning points, distance is 1 unit, not