Theory
A vector function is a function that is written as a vector. It looks like this:
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An important area of use for vector functions is position, velocity, acceleration and speed. The connection between these hasn’t changed from what you have learned earlier, but now you’re going to look at them as vectors. The only newcomer is speed, but don’t worry, it’s just the length of the velocity vector. If you want to know how fast the acceleration is, you can find that out by calculating the length of the acceleration vector.
Theory
The position vector:
The velocity vector:
The speed:
The acceleration vector:
The acceleration:
Example 1
An insect flying away from a flower is in the position
You can find the velocity vector by differentiating the position vector
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Next, you can insert
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From here it’s easy to find the speed as well, as it’s just the length of the velocity vector
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The length of that vector is
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giving you an acceleration of