Answer:
The position of the particle when it achieves its maximum speed in the positive x direction is 20 meters
Step-by-step explanation:
The position of the particle is given by the equation

The speed (v) of the particle is calculated as:

The acceleration of the particle is:

At maximum speed, the acceleration of the particle is zero
That is, a = 0
a = 12 - 6t
0 = 12 - 6t
6t = 12
t = 12/6
t = 2
This means that the speed of the particle is maximum at the time, t = 2
Substitute t = 2 into x = 6t² - t³
x = 6(2²) - (2²)
x = 6(4) - 4
x = 24 - 4
x = 20 meters
The position of the particle when it achieves its maximum speed in the positive x direction is 20 meters