Position Velocity Acceleration vectors - Derivatives

Problem Statement:

The position vector of a particle is given by: r = 3t i + 2t2  -2 (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/s2.

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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