**Problem Statement:**

The position vector of a particle is given by: **r** = 3t **i** + 2t^{2} **j ** -2 **k ** (m). Find its velocity and its acceleration.

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**Solution:**

The velocity vector of the particle is the time derive of its position vector:

The derivative of a sum is the sum of the derivatives, therefore:

The SI (International System) unit of velocity is m/s.

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The acceleration is defined as the derivative of the velocity:

The SI (International System) unit of acceleration is m/s^{2}.

As you can see, the acceleration vector does not depend on time, so the motion of this particle is ** uniformly accelerated **.

All the results of this problem are in units of the International System (SI).

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