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In previous videos, we looked at motion along a straight line, and now we're going to look at motion

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along a curved line, now curved line can be in two dimensions or it could be in three dimensions to

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generalize.

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We're going to look at motion along a curved line in three dimensions, which means you need three coordinates

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to describe this motion.

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So the way we do this is we define an origin and say that is the origin there and it's got coordinates

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zero zero zero and we have a particle that's going to move along some curved path, a certain distance

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from the origin.

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So this origin is point zero zero zero.

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And we're going to have a particle that moves along this curved line.

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It said that's our particle.

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Now, this particle is going to be a distance or from the origin.

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And that or is a vector, it's got three coordinates indicating the position of this particle, this

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particle can move and let's say this particle moves to here in a certain time and you can see that or

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is going to change.

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So the coordinates of or is going to change, let's call that or Brawne.

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And the direction of the velocity of this particle is also going to change in this case, the velocity

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is in the direction of a year, the velocity has changed.

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It's more in that direction.

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Again, this we need to describe.

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So, again, we're going to look at position, velocity and acceleration.

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Position we described by our.

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Position, position or.

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Is a certain amount X.

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In the eye direction unit, Victor, I certain in the X direction plus a certain amount in the direction

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plus a certain amount in the key direction.

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Now I.

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J and those are unit vectors in the X, Y and Z axis directions.

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So this is how we describe our position on if you work on a flat plane, like on the page of the there

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is no Z coordinates, it's only a certain distance along the X axis in the other direction and a certain

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distance along the Y axis and the Z in the direction.

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But I keep on adding the K direction because that is totally acceptable, that this particle can move

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in three dimensions.

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Now, here's the thing.

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If we take the time derivative of position, what do we get?

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We get velocity.

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So velocity.

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Velocity V and I add a little line there, because it is now a vector in three dimensions, three dimensions.

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It's going to be still the answer to it.

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Previously it was the HST, we just signify position with an Aurier when when we're not along a straight

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line, but along a curve path.

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And so that is just going to be the components, it's going to be the X, the T in the other direction,

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so there's a certain velocity in this direction.

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Plus the Y did it in the J direction, plus the Z, T in the K direction.

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And we can give an example of this is an example, example would be that our velocity of a certain particle,

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let's say this particle at this point has a certain velocity and that velocity could be something like,

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let's say three T.

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In the other direction, plus five T in the J direction plus two K.

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Plus two in the key direction.

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Sorry about that, so you can see it is a function of time.

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It doesn't necessarily have to be a function of time.

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It could always be, too, in the direction you of a team there.

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But the point I'm trying to make is that it is a function in three different directions.

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And we sort of have three independent equations, three independent components for the velocity in each

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one of the three principal directions, the I, J and K Direxion.

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So now the next one is acceleration.

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So.

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Let's look at acceleration.

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We know that acceleration is the term derivative of velocity acceleration, a time derivative of the

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velocity, sorry, my Vee's looked like an R sometimes, but it's a V.

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So that would be what is V. We have a we know that V is the first derivative of position in each direction.

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So we're going to have the derivative of so we're going to have Divi Deti, D.V. X, which is the X

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component of the velocity in the eye unit vector direction, plus the the Y T in the general direction

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plus the V Z, T in the K direction.

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So once again we have different components.

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Of the acceleration for each one of our directions age, OK?

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Now, what is the absolute acceleration, the absolute exhilaration, it's going to be the magnitude

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of these components and the way we calculate that is that we take the square root of each of the components.

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So that would be the square root.

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Now, instead of writing all of this, I'm just going to write a X, so we X.

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Squared plus a Y squared, there's a Z squared.

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So I take each one of these acceleration components, square them, take the square root to find the

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magnitude.