Velocity and displacement

Hey, Philip! Time for tennis? How far did you ride to get here? What was the distance? That's right, five kilometers.

Let's look at that on the map... Here is Philip's house. He leaves. Turns back and forth, and there he arrives. On the meter, it says five kilometers.

But you can also draw a straight line between Philip's house and the sports centre. -- As the crow flies. -- That's four kilometers. So, how far is it from the house to the sports centre? -- Five kilometers, -- or four kilometers? The answer depends on whether we want to describe the distance -- or the displacement. In everyday use distance and displacement seem to be the same; but in physics they represent precisely different things. The distance is the path Philip has followed, including all the twists and turns.

It's five kilometers; we saw that on his meter. The displacement is the most direct path between two points. We draw a straight line and measure. Four kilometers. The displacement is described with both a number - of meters - and a direction: directly from the starting point...

to the end point. Size, and direction. The distance doesn't have a direction. It's simply a length that's measured - perhaps a number of meters or kilometers. It takes Philip fifteen minutes to drive to the sports centre - a quarter of an hour.

The time is the same, regardless of whether we measure the distance or the displacement. What can we say about the speed? The speed is the distance divided by time. Five divided by a quarter of an hour... Becomes twenty kilometres per hour.

But wait! What happens if we divide the displacement - four kilometers - by the time? Would that give another result... ? Yes, indeed. That would calculate the average velocity.

Speed and velocity are different things in physics. Speed is calculated by dividing distance by time. Velocity - is displacement divided by time. And just as displacement has a direction, velocity has a direction. Velocity is shown as a number - kilometers per hour, say - and also an arrow - showing the direction.

Speed however, has no direction, just like distance. Do you see the pattern? Distance and speed do not have direction. Displacement and velocity do have direction. You with us, Philip?

But now it's tennis time, yes? Philip has finished playing tennis, and is going home. He drives the same path as he did to the sports centre. Hi again, Philip! Welcome home!

Let's review! What distance have you driven with the moped today? Check on the map again? Five kilometers to the sports centre. Five kilometers back.

Ten kilometers! But what is the displacement? The starting point is here. -- And the end point is... Yes. It's also right here. -- Philip is at home again.

And what happens if we try to draw a line from the starting point to the end point? Er... It can't be done. It's the same point... And there'll be no line.

The displacement is... zero! The distance is ten kilometers, but the total displacement is zero. He's gone to the sports centre, played tennis, gone home... But still the displacement is zero, because he's back at the same place he started from.

What does this mean for the velocity, Philip? Yes. If you are back at the same point, the displacement is zero. Then the average velocity is zero, no matter how fast you rode. Oh...

You're off again? Whoops. Out of petrol? Yes. Although your net displacement is zero, you might still burn petrol.