Problem Description
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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.