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Let's talk about kinetic energy.

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We're calling kinetic
energy K, and it's

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given by 1/2mv squared.

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And this is a scalar quantity.

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So it's going to be
either 0 or positive.

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It's never going to be negative.

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The SI unit for kinetic
energy is joule,

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so we have one joule
here for kinetic energy.

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And the units come from this,
so we have kilogram and then

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meter per second squared.

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Now, let's assume we have an
object that is first at rest

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and then it speeds up with
a certain velocity, which

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means the object is
going to experience

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a change in kinetic energy.

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And so we'll express this
as 1/2mv final squared

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minus 1/2mv initial squared.

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And if we have a
motion, so velocity in,

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let's say a 2D or
a 3D space, then

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we have to consider all
these components here

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and we can also
pull out the 1/2m,

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and then we have
vx final squared

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plus vy final squared
plus vz final squared

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and then minus all the initial
values, x initial, y initial,

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and z initial.

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Now when we consider
just a point particle,

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then we can also ask
what is the momentum?

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How can we pair up momentum
and kinetic energy?

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So I'm writing it again
here, k equals 1/2mv squared.

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If we multiply this by m
upstairs and downstairs,

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we're going to have m
squared over v squared,

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and that's actually p squared.

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Remember p equals mv.

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And so we're going to get that
this actually can be expressed

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as p squared over 2m.

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And so that is
the kinetic energy

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expressed in terms of the
momentum of a particle.