We've come to the Porsche
Experience Center Test Track
to talk about
speed and velocity.
And if we're
gonna do so,
we might as well
make it interesting.
 (engine revving)
♪♪
In our daily lives,
we may use the terms speed
and velocity interchangeably.
But in physics,
speed and velocity
are two very
different things.
In this segment,
we're gonna find out
how and why this
difference matters.
The cars speeding behind me are
moving with a lot of speed,
 but what does
 that mean?
 Speed is the rate at which
 an object covers distance.
 The SI unit for speed
 is meters per second.
 It's a scalar quantity,
 meaning it only
 has a magnitude.
For scalar quantities
such as speed,
the direction the object is
moving in doesn't matter.
 If the car keeps moving just
 as fast as it was before,
 except this time it's going
 the opposite direction,
its speed still
remains the same.
Just because the car is moving
in the opposite direction
doesn't mean the
speed is negative.
 Speed will always
 be a positive value.
We calculate the average
speed of an object
by using this equation.
The average speed
in meters per second
is equal to the total
distance traveled, in meters,
divided by the total
time taken, in seconds.
 Let's work through
 an example.
 When a car makes a lap
 around the track,
 we can calculate
 its average speed
 using the distance it traveled
 and how much time it took.
 One lap around this track
 is 1600 meters,
 and the time it takes
 this car is 55 seconds.
 So the average was 1600 meters
 divided by 55 seconds,
 which is 29.1
 meters per second.
 That's pretty fast.
Okay, we've talked about
speed as a scalar quantity.
What about velocity?
 Velocity is a
 vector quantity.
 It means it not only
 has a magnitude,
 but it also
 has direction.
The SI unit for velocity
is also meters per second.
So when a car
speeds past again,
 its speed is
 71 miles per hour,
 or 30 meters
 per second.
 But its velocity is 30 meters
 per second going right.
Average velocity is an
object's change in position,
or displacement,
over change in time.
We can calculate it
using this equation.
 An object's average velocity
 in meters per second
 is equal to its
 change in position,
 or its displacement,
 in meters,
 divided by the change
 in time, in seconds.
 When solving this problem
 with velocity,
 it's important to establish
 a frame of reference.
Let's go to the track
for an example.
Say that right is
the positive direction,
and left is the
negative direction.
 A car is stationary at
 our origin point, point A,
 facing right.
 It's going to speed
 towards point B,
 and turn around to stop
 halfway back to point A
 at point C.
Would the average speed
and the average velocity
of the car over this
journey be the same?
 Well, there's only
 one way to find out.
 It took the car 7 seconds
 to complete its journey.
 The total distance it
 traveled was 24 meters.
 This means that the average
 speed was 24 meters
 divided by 7 seconds,
 which is 3.43
 meters per second.
 However, the total distance
 traveled by the car
 is different from
 the total displacement.
 The car's displacement
 only takes into account
 the point-to-point
 difference, in meters,
 between the origin and
 the final destination.
 The displacement from
 point A to point C
 is 8 meters.
 This means that the average
 velocity over the journey
 is positive 8 meters
 divided by 7 seconds,
 which is positive
 1.14 meters per second,
 or 1.14 meters per
 second to the right.
 So it's possible for
 the average speed
 and the average velocity to
 have two separate values,
 even for the
 same journey.
To recap, speed is
a scalar quantity,
which means it has
magnitude only.
Velocity is a
vector quantity,
meaning it has both
magnitude and direction.
But how are we supposed to know
which direction is positive
and which direction
is negative?
Good news.
It's our choice.
We pick our own negative
and positive directions.
So when you're given
a problem to solve,
indicate which direction
you've picked to be positive.
Whatever answer you get
should reflect that choice.
 We usually treat right
 and up as positive,
 and left and down
 as negative.
 So when the car was going
 from point A to point B,
 it was traveling in
 a positive direction
 because we designated right
 as the positive direction.
 If the car went from
 A to B in 4 seconds,
 then its average velocity
 was 4 meters per second
 going in the
 positive direction.
 But when the car was going
 from point B to point C,
 it was facing
 the other way.
 If it did so
 in 3 seconds,
then it had an average velocity
of 2.67 meters per second
 in the negative direction.
Now, let's talk about
the difference between
average velocity and
instantaneous velocity.
Average velocity,
as we've been discussing,
is the displacement divided
by the change in time.
We calculated the average
velocity of the car
going from point A
to point C.
But what about the
journey itself?
The average velocity tells
us the overall velocity
over the course of
the entire journey.
The instantaneous velocity
is the velocity of an object
at a specific
point in time.
 Let's look at the car as it
 was starting to accelerate
 and freeze it
 right there.
 At the time
 0.5 seconds,
 its instantaneous velocity
 is 3.27 meters per second
 to the right.
 As the car speeds up,
 its velocity increases.
 What if we sped up to
 right here, at 1.5 seconds?
 Its instantaneous velocity is
 now 9.81 meters per second
 to the right.
 Remember, the
 instantaneous velocity
 is the velocity of an object
 at a specific moment in time.
Another important term to
know is constant velocity,
which is what we call
unchanging velocity.
Okay, so we've learned
what velocity is,
whether it's average,
instantaneous, or constant.
But how do we
represent it?
 If we have a
 position time graph,
 we can use it to learn
 about an object's velocity.
 In a position time graph,
 the time elapsed will
 be shown on the X axis,
 and its position
 shown on the Y axis.
 This graph shows
 a constant velocity,
 which, on a position
 time graph,
 looks like a
 straight line.
 By looking at the
 slope of the line
 in a position time graph,
 we can learn about
 an object's velocity.
 It makes sense that
 this object is moving
 at a constant velocity,
 because the slope of the
 line is not changing.
We're covering the same
amount of distance
in the same
amount of time.
We can calculate the
constant velocity
 by finding the
 slope of this line.
 If the velocity
 wasn't constant,
 we can calculate the average
 velocity by drawing a line
 between two points in time
 and find out the
 slope of that line.
 If we want to know the
 instantaneous velocity,
 or our velocity at
 a given point in time,
 we can draw a tangent line
 from that point in time
 and find the slope
 of the tangent.
 We can also have graphs
 that look like this,
 with the line
 going up and down.
This point indicates I'm moving
in the positive direction,
 away from my origin.
 This would be me moving
 at a constant velocity
 away from my origin in
 the position direction.
 This point right here would
 indicate me turning around
 and moving at a
 constant velocity
 in the negative direction.
 It doesn't mean that I'm
 going any slower or faster.
 The negative slope just
 means that I'm moving
 back toward the origin
 in the negative direction.
Remember, the slope of a line
on a position time graph
tells us the velocity
of the object.
For a more detailed analysis
of position time graphs,
see Unit 2, Segment D
on Graphing Motion.
We've talked
about speed
and how to calculate the
average speed of a journey
using distance covered
and the time taken.
We talked about the
difference between
speed and velocity.
And the differences between
instantaneous velocity,
constant velocity,
and average velocity.
We've also looked at how
we can deduce magnitude
and the direction
of velocity,
both average velocity and
instantaneous velocity,
by looking at the slope of a
line on a position time graph.
That's it for this segment
of "Physics in Motion".
I've enjoyed myself.
I hope you have, too,
and we'll see you next time.
 For more practice problems,
 lab activities,
 and note-taking guides,
 check out the
 "Physics in Motion" Toolkit.
