The position of a particle moving along the x axis is given by x = 6.0t2 − 1.0t3, where x is in meters and t in seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction?
A)24 m
B)12 m
C)32 m
D)16 m
E)2.0 m

Question

Quizplus · Accepted Answer

The speed of the particle is given by the first derivative of the position function: v = 12t - 3t^2. The particle achieves its maximum speed when this derivative is equal to zero. Solving for t, we get t = 4 s. Substituting this value of t back into the position function, we get x = 6(4)^2 - 1(4)^3 = 16 m. Therefore, the correct answer is D.

The Position of a Particle Moving Along the X Axis