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- [Instructor] Pretend
you are a physics student.

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You are just getting out of class.

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You were walking home when you remembered

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that there was a Galaxy
Wars marathon on tonight,

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so you'd do what every
physics student would do: run.

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You're pretty motivated to get home,

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so say you start running
at six meters per second.

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Maybe it's been a while
since the last time you ran,

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so you have to slow down a little bit

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to two meters per second.

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When you get a little
closer to home, you say:

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"No, Captain Antares wouldn't give up

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"and I'm not giving up
either", and you start running

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at eight meters per second
and you make it home

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just in time for the opening music.

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These numbers are values
of the instantaneous speed.

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The instantaneous speed
is the speed of an object

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at a particular moment in time.

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And if you include the
direction with that speed,

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you get the instantaneous velocity.

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In other words, eight meters
per second to the right

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was the instantaneously
velocity of this person

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at that particular moment in time.

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Note that this is different
from the average velocity.

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If your home was 1,000
meters away from school

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and it took you a total of
200 seconds to get there,

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your average velocity would
be five meters per second,

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which doesn't necessarily equal
the instantaneous velocities

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at particular points on your trip.

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In other words, let's
say you jogged 60 meters

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in a time of 15 seconds.

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During this time you were
speeding up and slowing down

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and changing your speed at every moment.

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Regardless of the speeding
up or slowing down

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that took place during this path,

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your average velocity's
still just gonna be

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four meters per second to the right;

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or, if you like, positive
four meters per second.

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Say you wanted to know
the instantaneous velocity

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at a particular point in
time during this trip.

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In that case, you'd wanna
find a smaller displacement

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over a shorter time interval

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that's centered at that
point where you're trying

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to find the instantaneous velocity.

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This would give you a better value for

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the instantaneous velocity but
it still wouldn't be perfect.

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In order to better zero-in on
the instantaneous velocity,

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we could choose an even
smaller displacement

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over that even shorter time interval.

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But we're gonna run into a problem here

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because if you wanna find a perfect value

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for the instantaneous velocity,

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you'd have to take an
infinitesimally-small displacement

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divided by an infinitesimally-small
time interval.

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But that's basically zero divided by zero,

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and for a long time no one
could make any sense of this.

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In fact, since defining motion
at a particular point in time

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seemed impossible, it made
some ancient Greeks question

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whether motion had any meaning at all.

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They wondered weather
motion was just an illusion.

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Eventually, Sir Isaac Newton developed

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a whole new way to do math that lets you

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figure out answers to
these types of questions.

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Today we call the math that
Newton invented calculus.

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So if you were to ask a physicist:

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"What's the formula for the
instantaneous velocity?",

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he or she would probably give you

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a formula that involves calculus.

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But, in case some of you
haven't taken calculus yet,

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I'm gonna show you a few ways to find

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the instantaneous velocity
that don't require

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the use of calculus.

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The first way is so simple
that it's kind of obvious.

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If you're lucky enough to have a case

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where the velocity of an
object doesn't change,

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then the formula for average
velocity is just gonna give you

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the same number as the
instantaneous velocity

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at any point in time.

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If your velocity is changing,

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one way you can find the
instantaneous velocity

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is by looking at the motion
on an x-versus-t graph.

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The slope at any particular point

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on this position-versus-time graph

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is gonna equal the instantaneous velocity

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at that point in time because

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the slope is gonna give
the instantaneous rate

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at which x is changing
with respect to time.

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A third way to find the
instantaneous velocity is for

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another special case where
the acceleration is constant.

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If the acceleration is constant,

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you can use the Kinematic Formulas

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to find the instantaneous
velocity, v, at any time, t.

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(electronic music)