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Check out these weightlifters.

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The one on the right is
lifting his weight faster,

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but they're both doing
the same amount of work.

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The reason I can say
that is because work

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is the amount of energy
that's transferred.

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Or to put it a
simpler way, this is

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the way I like to
think about it,

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work is equal to
the amount of energy

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you give something or
take away from something.

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Both weightlifters are
giving their weights

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the same amount of
gravitational potential energy.

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They both lift them two
meters, and the masses

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are 100 kilograms each.

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Plug those into the formula for
gravitational potential energy,

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and you find that the work
done by each weightlifter

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is 1,960 joules.

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But the weightlifter
on the right

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is lifting his weight faster.

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And there should be
a way to distinguish

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between what he's doing
and what the other slower

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weightlifter is doing.

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We can distinguish
their actions in physics

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by talking about power.

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Power measures the
rate at which someone

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like these weightlifters or
something like an automobile

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engine does work.

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To be specific, power is
defined as the work done

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divided by the time that
it took to do that work.

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We already said that
both weightlifters

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are doing 1,960 joules of work.

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The weightlifter on the
right takes 1 second

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to lift his weights, and
the weightlifter on the left

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takes 3 seconds to
lift his weights.

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If we plug those times into
the definition of power,

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we'll find that the power
output of the weightlifter

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on the right during his lift
is 1,960 joules per second.

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And the power output
of the weightlifter

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on the left during his lift
is 653 joules per second.

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A joule per second
is named a watt,

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after the Scottish
engineer James Watt.

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And the watt is abbreviated
with a capital W.

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All right, let's look
at another example.

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Let's say a 1,000 kilogram
car starts from rest

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and takes 2 seconds to reach a
speed of 5 meters per second.

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We can find the power
output by the engine

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by taking the work
done on the car divided

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by the time it took
to do that work.

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To find the work
done on the car,

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we just need to figure
out how much energy

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was given to the car.

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In this case, the car
was given kinetic energy

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and it took two seconds to
give it that kinetic energy.

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If we plug in the values
for the mass and the speed,

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we find the engine had a
power output of 6,250 watts.

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We should be clear that what
we've really been finding here

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is the average power
output because we've

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been looking at the total
work done over a given time

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interval.

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If we were to look at
the time intervals that

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got smaller and smaller, we'd
be getting closer and closer

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to the power output
at a given moment.

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And if we were to make our time
interval infinitesimally small,

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we'd be finding the power
output at that particular point

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in time.

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We call this the
instantaneous power.

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Dealing with
infinitesimals typically

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requires the use of
calculus, but there

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are ways of finding
the instantaneous power

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without having to use calculus.

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For instance, let's
say you were looking

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at a car whose
instantaneous power output

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was 6,250 watts at
every given moment.

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Since the instantaneous
power never changes,

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the average power just equals
the instantaneous power,

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which equals 6,250 watts.

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In other words, the average
power over any time interval

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is going to equal the
instantaneous power

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at any moment.

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And that means work
per time gives you

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both the average power and
the instantaneous power

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in this case.

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Let's say you weren't so lucky,
and the instantaneous power

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was changing as
the car progressed.

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Then, how would you find
the instantaneous power?

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Well, we know that power
is just the work per time.

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So something we
can try is to plug

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in the formula for work, which
looks like FD cosine theta,

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and then divide by the time.

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Something that you might
notice is that now we

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have distance per
time in this formula.

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So let's isolate the
distance per time.

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Distance per time
is just the speed.

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So I can replace d over
t with v in this formula.

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And if you plug in the
instantaneous speed of the car

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at a given moment
in time, you'll

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be finding the
instantaneous power output

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by the force on the car at
that particular moment in time.

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So to find the instantaneous
power output by a force,

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plug in the force on the object
at a particular moment in time,

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multiply by the
speed of the object

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at that same moment in time,
then multiply by cosine theta.

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But be careful here.

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Theta isn't any old angle.

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It's the angle between
the force on the object

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and the velocity of the object.

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But in many cases, the force
is in the same direction

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as the velocity, which means
the angle between the force

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and the velocity is zero.

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And since cosine of 0
is 1, you don't really

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need the cosine in
the formula at all.

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And you find that the
instantaneous power is just

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the force times the speed.

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All right.

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So what does power mean?

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Power is the rate at
which work is done.

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What does average power mean?

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Average power is the work done
divided by the time interval

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that it took to do that work.

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What does the
instantaneous power mean?

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Instantaneous power
is the power output

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of a force at a
particular moment in time.

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