Speed and Velocity

I'm Joe Crane from the University of Leicester,

and in this course I'm going to talk to you about cinematics.

What we're going to do is describe the motion

of bodies without worrying about what causes that motion.

So we'll talk about distance, time, speed, acceleration.

Now

I want to watch this ball

describe what you saw.

Now be honest.

What you actually saw was that the ball

seemed to hover for a moment,

and then in some way it gathered speed.

But it was quite difficult to describe exactly what was going on.

That's because we need some rather detailed measurements

to see how we can describe that motion.

So we're going to start with something simpler.

We're going to start just by looking at speed

and velocity.

So here are some examples of speed

human hair growth,

um, up to the speed of light in a vacuum.

Now it's often not convenient to talk about the speed of human hair growing at

100 millionth of a mile an hour.

What we normally try and do is use units in which

everything that everything has a magnitude somewhere between one and 10.

So his little exercise for you

show that human hair grows at about one nanometer per second,

give or take thereabouts,

so those are examples of average speed. What we mean by average speed.

We mean the distance

the object has travelled, divided by the time it's taken to travel that distance.

So we can say that the average speed is distance divided by time.

And we can use symbols to describe that we can

use the symbol s for distance V for velocity or speed

and t for time so that we can say that V is s divided by t

and we can manipulate that formula so that distance is velocity times, time

and time is distance divided by velocity or speed.

Now the important thing is that these are

not formula that are somehow invented for physics.

These are formula that express things that you're quite familiar with.

So let's say you were earning pocket money or wages.

Let's save very generous, let's say, £5 an hour.

So if you work for three hours, you know, £5 an hour at three hours you learned £15.

The amount you earn is the rate at which you're earning times the time.

It's exactly the same in physics.

When we're talking about the distance is the rate of change of distance,

times the time.

So these formula aren't something special that you

have to learn just in the physics class.

They express the way the world is in symbols

which is sometimes very convenient to increase our understanding.

Now, in English,

we distinguish between speed and velocity and

many other European languages You don't,

but in English, we mean by speed just the magnitude

of the rate of change of distance with respect to time.

Whereas in velocity, we say what direction that changes in. So velocity is speed

and the direction

that means that we can compose a velocity into various components.

So we see here that the velocity in this

direction is composed of two components the horizontal component

and a vertical component. Now, why is that?

Well, if we think of travelling along the diagonal hypothesis of this triangle,

we can arrive at the same place by travelling along the two sides.

So the distances displacements add up

in this way.

But velocity

is just displacement divided by time.

So if the displacements add up in this way,

so too will the displacements divided by time

and we can

decomposed velocity into two components,

Or we can combine components to form the overall velocity.

You can do that in three dimensions as well,

although that's slightly more complicated.

Here's another way in which we can get a picture of a body moving at constant speed.

That's to say, to draw a graph.

So here we have a graph

of velocity against time

and distance against time.

So I haven't specified the unit here because I want to draw

distance and speed on the same graph.

Let's imagine the bodies moving with the speed of one unit,

constant speed of one unit along here.

So that's a straight line,

and

we can express the distance travelled by

noting the distance will increase uniform from zero

up to 10 units after a time of 10 units.

And what we can see on this picture

is that the speed

is the slope of this distance graph.

So if we take time displacement of two units here, a space

displaced for the distance of two units there to over two is one

and one unit of distance per unit. Time is the speed at which the body is moving.

We can also say that the distance is the area under this speed curve. So say, after six

units of time here, the

body will have moved here six units of distance.

Because this area under here is one time six, which is just six

in this section.

Then we've looked at constant velocity in the next section

will go on to look at something more complicated,

constant acceleration.