A robotic arm on an assembly line handles delicate components. To properly place these components, the position of the arm must be specified as a function of time. If, however, the acceleration of the arm is too great, the components may be damaged.

What is known:

• The arm moves along a linear path.
• The position of the arm is given by
  
  x(t) = 0.3 t² - 0.2 t³ m   for 0 ≤ t ≤ 1.5 seconds

Knowing the position of the arm as a function of time,

1. What is the velocity as a function of time?
2. What is the acceleration as a function of time?
   

• Analyze the rectilinear motion of a particle to determine the relationship between position, velocity, and acceleration.
• Use differentiation to determine the velocity and acceleration of the arm.