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.