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 t^{2} - 0.2 t^{3} m for 0
≤ t ≤
1.5 seconds

Questions

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

What is the velocity as a function of time?

What is the acceleration as a function of time?

Approach

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.

Practice Homework and Test problems now available in the 'Eng Dynamics' mobile app
Includes over 400 problems with complete detailed solutions.
Available now at the
Google Play Store and
Apple App Store.