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 :

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 :

G1 Physics · Accepted Answer

The position is x(t) = 4t³-3t. To find when the particle returns to the origin, set x = 0: 4t³-3t = 0. Therefore, t(4t²-3) = 0. For t > 0, t = √3/2 ≈ 0.866. Hence statement A is true. Velocity is v = dx/dt = 12t²-3. At a turning point, v = 0. Thus, 12t²-3 = 0, so t = 1/2. Position at this instant is x = 4(1/2)³-3(1/2) = 1/2-3/2 = -1. Therefore the particle is 1 unit away from the origin. Statement B is true and statement D is false. Acceleration is a = dv/dt = 24t. For t ≥ 0, a ≥ 0. Hence st…