Lesson video

Hello there.

My name is Mr. Forbes.

And welcome to this lesson from the Moving by Force unit.

This lesson's all about how to measure speed accurately, and in it we'll be looking at how to use devices to measure speed and how to reduce the sorts of errors that you'll make with measuring time, and that will allow us to measure speed more accurately.

By the end of this lesson, you're going to be able to describe how to measure speed accurately, and by that I mean how to measure the average speed of an object and how to measure something called the instantaneous speed, the speed at a particular point in time.

This is the set of keywords that you'll need to understand to get the most out of the lesson.

The first of these is average speed, which you should have seen before.

The average speed is the distance divided by time.

The second is a new concept and it's instantaneous speed, and that's the speed you're traveling at a particular moment.

Third is timing error, and these are the types of error you get whenever you're using some sort of stopwatch or timer.

And random error is the last of them, and that's an error that you can't control.

It can be higher or lower than the true value.

And here are the definitions of those keywords.

You can refer back to this slide at any point in the lesson if you need to check them again.

This lesson's in three parts, The first part's about the difference between average and instantaneous speed.

The second part is about how we can measure the top speed of an object and getting an approximation of an instantaneous speed.

And the third part is about spotting and reducing timing errors that you might have during any experiment.

So, let's go on with the first part, instantaneous and average speed.

Now you've probably seen this equation before.

The average speed of an object is the total distance it travels divided by the total time it took to cover that distance.

And by average speed we're always talking about the mean average, a particular type of average.

So if a sprinter runs 100 meter race in 10 seconds, we get an average speed of 10 meters per second.

That's 100 meters divided by 10 seconds is equal to 10 meters per second.

This car travels 120 kilometers in two hours.

So to find the speed of that we can divide the distance by the time, 120 kilometers divided by two hours gives us an average speed of 60 kilometers per hour.

When you're traveling along, for example in a car, your speed doesn't always stay the same.

It regularly changes as you speed up and slow down due to traffic.

Your speed at any particular moment in that journey is called the instantaneous speed.

That literally means the speed at a particular instant.

So during the 100 meter race, you might have instantaneous speeds like this.

Just before you start and at the instant you start, you're not moving, so you'd be traveling at 0 meters per second.

As you run the race and get faster and faster, you might reach an instantaneous speed of 8 meters per second.

And then when you approach the finish line and get a bit tireder and slow down a little, you might only be traveling at 7 meters per second.

So you can see the instantaneous speed has changed throughout the race as you get faster and slower.

We can still calculate your average speed using the time it took you to finish the race.

The highest of those instantaneous speeds is the top speed.

So you can see from the data I've given you there, halfway through the race they were traveling at 8 meters per second and that's their top speed.

Now, you've probably seen a device like this before.

This is a speedometer and it's used in cars and motorcycles to show your instantaneous speed, how fast you're traveling at a particular moment.

This speedometer has got two separate scales, one in kilometers per hour, one in miles per hour.

In the UK we typically use miles per hour.

In a normal journey, your speed is gonna change continuously as you speed up and slow down due to traffic.

So for example, at traffic lights, you'll be traveling, well, you'd be stopped, so 0 miles an hour.

Then as the traffic lights change green, you might accelerate away and reach speeds of 30 miles per hour, which is the maximum speed on normal roads.

And if you reach a motorway, you might be able to accelerate again and go at speed up to 70 miles an hour, the maximum speed on a motorway.

And the speedometer will show you the speed you're traveling at any point in that journey.

It won't show you the average speed, it'll show you the instantaneous speed.

Right, we've got a check for you now.

Is this true or false?

The instantaneous speed is always the same as the average speed.

I'd like you to pause the video, make your selection, and then restart.

Okay, you should have chosen false there, but what's the reason for that answer?

Is it A, the instantaneous speed is always less than the average speed?

Or is it B, the instantaneous speed can be higher or lower than the average speed?

So pause again, make your selection, and then restart.

Right, the answer you should have given that one is the instantaneous speed can be higher or lower.

You can be traveling at a high speed or a low speed.

The average speed will just average all of those out.

So well done if you got that.

You might have used dynamics trolleys in previous lessons for experiments in measuring speed, and we're gonna talk about one of those again now.

if you've got a dynamics trolley rolling down a ramp, it speeds up as it rolls.

So at the start, before you release it, it's got an instantaneous speed of 0 meters per second.

It's not moving at all.

And then once it's released, it will gradually get faster and roll towards the end.

So here at the finish line, we've got an instantaneous speed of two meters per second.

During its journey, it increased its speed from 0 meters per second to 2 meters per second.

So at any point in that journey, its instantaneous speed will be somewhere between those two values.

So the average speed will also be between those two values.

I'd like to check that you understood what I said there.

So I've got another example here.

A trolley rolling down a ramp is stationary at the start and at the finish line, its instantaneous speed is 3 meters per second.

Which of these would be its average speed?

So pause the video, make your selection, and then restart.

Okay, as we said earlier, the average speed is gonna be somewhere between the starting speed and the end speed when it's rolling down the ramp.

And the only value that fits that is 1.

5 meters per second.

So well done if you've selected that one.

This is a picture of Florence Griffith-Joyner and she's the world record holder for the 100 meter sprint.

We can calculate her average speed from the distance and time and information, but we can also examine her instantaneous speed during the race, and that's what I'd like you to do.

I'd like you to fill in the gaps to describe Flo-Jo's world record breaking 100 meter race.

I'd like you to only use the words average and instantaneous.

So I want you to read through the rest of the information on that page, the three paragraphs, looking at the gaps, I'd like you to fill those in using the words average or instantaneous, and you can use those words as often as you want.

So pause the video, fill in the gaps, and restart and I'll go through it with you.

Okay, let's have a look through and see what the answers were.

In 1998, Flo-Jo ran the 100 meters in 10.

49 seconds and set a new world record.

Her average speed for the race was 9.

5 meters per second.

We got that information from the distance and time there.

As the starting gun went off, her instantaneous speed was zero, she wasn't moving, she quickly sped up and at the 50 meter point, her instantaneous speed was 11 meters per second, and for the first half of the race, her average speed was 8.

6 meters per second.

So we can find the average speed for that first section.

After the halfway point, Flo-Jo slowed a little.

Her average speed for the second half of the race was 10.

7 meters per second.

In the last few meters, she sped up again and on the finish line, her instantaneous speed was 11.

2 meters per second.

That was quite a difficult task.

So well done if you got all of those correct.

Okay, now we're gonna move on to measuring top speed.

We're gonna describe an experiment about measuring that speed over a very short distance so we get an approximation of an instantaneous speed as well.

As I mentioned earlier, the speed of a trolley increases as it rolls down a ramp.

There's a force acting on the trolley and that force keeps speeding the trolley up until by the end of the ramp it's reached its highest speed.

So its highest speed will be just as the trolley reaches the end of the ramp and the force has accelerated it to its maximum.

Let's check if you understood what I explained there.

Why is the trolley moving faster at the bottom of the ramp than at the top?

Is it A, the ramp is flatter at the end than the start?

Is it B, the resulting force is speeding up as it travels?

Or as it C, the resultant force slows it down as it travels?

Okay, the answer to that was B, the resultant force is speeding up as it travels.

Well done if you got that.

That force continues to act on the trolley and that makes it get faster and faster and faster until it reaches the end.

As we just described, the trolley's going to be moving at its top speed when it's near the end of the ramp.

So if we want to measure that top speed, we'll need to measure a distance and the time on the trolleys close to the end.

So we can put out two markers a few centimeters apart like this, and measure the distance between them and that will give us a distance measurement.

And when we release the trolley, it will be traveling near its top speed as it passes between the two markers.

The other thing we'll need to do is to measure the time it takes for it to pass between those markers, and for that we can use some sort of electronic timing device.

So let's have a look at how we can calculate the speed using time and distance information now.

So imagine we had a trolley near the top of a ramp and it took 0.

25 seconds to travel 10 centimeters.

Can we calculate the speed of the trolley?

Yes we can.

The first thing we need to do is to convert that distance into meters because we'll want an answer in meters per second.

10 centimeters is 0.

10 meters.

Next, we need the speed equation.

That's speed equals distance divided by time.

And all we need to do then is substitute in the distance and time values from the question.

So the speed is 0.

10 divided by 0.

25, and that gives us a final speed of 0.

4 meters per second.

Okay?

Okay, you should have followed the same process as I followed there, converting the distance into meters and using the speed equation.

So the distance was 0.

05 meters, that's five centimeters.

And the speed equation is there, speed equals distance divided by time.

Putting the values in from the question, speed equals 0.

05 divided by 0.

10, and that gives a speed of 0.

5 meters per second.

So the trolley's traveling faster at the bottom of the ramp than it was traveling at the top.

It is what we expected.

So for the second task of the lesson, I'd like you to think about how you'd measure the top speed of a sprinter from your class.

I've got 12 different things you could do to help measure that speed, but not all of them are necessary.

I'd like you to read through those and put the stages in the right order that you'd be able to measure the top speed of a sprinter.

I can tell you four of those aren't actually needed.

So I'd like you to pause the video, put those stages in order and then restart when you're ready.

Okay, here are the stages I'd use to measure the top speed of somebody sprinting.

First of all, I'd use a tape measure and I'd use that to measure our distance.

Now I wanna measure out a fairly small distance because most sprinters can't keep up the top speed for very long.

So a distance of 10 meters would be suitable, maybe even 5 meters.

I'd mark the start and finish lines with some sort of poles so we can see them easily.

Then I'd let the runner have a run up because they're not gonna start at the top speed.

They need to accelerate and get up to that top speed.

So I'd let them have maybe a 20 meter run up.

I'd use the timer to measure the time it takes them to run through those two power points, the start and the finish of those 10 meters.

And then I'd calculate their speed by dividing the distance by the time.

Because they've only done it once, there might be some sorts of error in my measurements.

So what I'd like to do is to repeat that to get an average time and then I could use that to get my calculation a bit more accurate.

I wouldn't need to put the sprinter at the start line, that wouldn't allow them to get to their top speed and I shouldn't need to count down to the start because they're getting a run up.

I can watch them approach the start line.

So I don't need a countdown.

And I don't need to divide the time taken by 10 and I don't need a meter rule.

A tape measure would be much better.

So well done if you've got those stages.

Okay, we've reached the final part of the lesson now and this is all about spotting and reducing timing errors during experiments.

So I carried out an experiment where I rolled the trolley down a ramp and three students observed that and tried to measure how long it took the trolley to pass between the start and the finish line, but they all got different results.

Issy said it took 3.

24 seconds for the trolley to roll down.

Andeep said it's 3.

28 seconds and Laura said it was 3.

31 seconds.

They'd all got slightly different values there.

Each of them has made some sort of timing error.

A timing error is a type of error that can't fully be avoided.

It's to do with your reaction time or your observation position and you don't measure the exact time precisely.

Let's see if you understand what a timing error is.

We've got four pupils and they're all trying to stop a timer on exactly 20 seconds.

And the results are here.

Laura took 20.

07 seconds.

Issy 20.

08.

Andeep, 20.

11, and Jacob 19.

98 seconds.

And what I'd like you to do is to decide which of those students produced the smallest timing error and which produced the largest timing error.

So pause the video, make your decision and restart when you're ready.

Okay, the students were asked to stop the timer on exactly 20 seconds.

So the one who's got the smallest timing error is the person who's closest to that value and that was Jacob.

He was only 0.

02 seconds out, that's pretty good.

The largest timing error was Andeep.

He was a whole 0.

11 seconds out, which is a much larger timing error.

Well done if you spotted those two.

So let's talk about the sources of some of those timing errors.

First of them is a random error due to the fact I'm not starting or stopping the stopwatch at exactly the right time.

When I'm observing anything, I might be anticipating when something's gonna start.

I might start the stopwatch a little bit early or I might have slow reaction time and stop it a little bit too late.

So it's impossible to predict if my measurements can be a little bit too big or a little bit too small.

For example, Laura here, timed an event and it's 3.

00 seconds exactly, but then she watched the same event again and it was 3.

11 seconds.

And the third time she tried to time the exact same thing was 2.

97 seconds.

So three different measurements for exactly the same thing.

That is a random error, it's unpredictable and she can't fully control that.

With practice, she might be able to eliminate some of it, but she's never gonna completely eliminate those random errors.

Random errors pop up in all sorts of measurements, not just timing ones.

So let's have a look at another example of that.

I've got pupils trying to measure the height of somebody using a tape measure and they all get slightly different distances, so slightly different heights.

Laura gets 120.

5 centimeters for the height.

Issy, 119.

8.

Andeep, 121.

2 and Jacob 120.

7.

What I'd like you to do is to explain what could be causing that random error in the measured height.

So pause the video, write down your explanation, and then restart.

Okay, let's have a look at some possible reasons for those differences in the measured height.

Your suggestions could have been something like this.

First of all, the tape measure could have been bent.

If you are trying to measure the height of somebody and they just stood in the middle of the room, that take measure is gonna be flexible and you're not gonna be able to measure precisely to the top of somebody's head.

A better way would be to make them stand against the wall, put a mark where the top of the head reaches and move them out the way and measure it just with the tape measure vertically then.

The other thing that could be happening is you are looking at slightly different angles.

If you're shorter than the person you're measuring, you are looking upwards at them and you might misread off the tape measure.

And if you're taller than them you're looking slightly downwards towards the tape measure and that would give you a slightly different reading as well.

So well done if you've got either of those possibilities.

One way to reduce timing error is to make sure you start the stopwatch at precisely the right time.

And to do that you can use a countdown.

If you're starting an object from stationary like a trolley and releasing it, you can count down 3, 2, 1, go!

And that will allow you to start the stopwatch as soon as you say "Go" or somebody else who's doing the observation to hear the "Go" and start their stopwatch then, and that will give a precise start time.

Measuring the finish time precisely is a bit more difficult because the object will be moving and you're watching a moving object pass the finish line.

To be able to measure that time accurately, you really need to be in line with the finish line so you can observe when the front or the back of the trolley passes the line.

So if you're looking directly along that line, you'll see the front of the trolley pass it and you'll be able to stop the stopwatch.

But, if you're slightly to the side like this, you're going to actually see the edge of the trolley pass the finish line before it's really reach there.

Or if you're observing from the other side of the finish line, again, you're gonna get a timing error and measure the wrong time.

You could be a fraction of a second out.

So always try and keep your head directly in line with the finish line if you want to get precise value.

You're never gonna be able to completely eliminate random timing errors when using a stopwatch, but one way you can improve your measurements is to video record the experiments.

That'll allow you to slow down time and take readings when you've paused the video.

So here's a trolley at a start line, and I've taken a video and then I've got a still of that and I've got a stopwatch there.

And here's a picture of the trolley passing the finish line a fraction of a second later.

Now if I zoom in and look closely at those two times, it passed the start line at 2.

36 seconds and it passes the finish line at 4.

37 seconds.

And I've got stills of that, so it's very easy for me to look and see the times and then calculate the time it took to pass between those two lines.

I subtract the values from each other and I get 2.

01 seconds.

So a much easier way of measuring the time accurately.

Okay, I've got some readings here from a digital timer and I'd like you to work out the time it takes a trolley to pass between the start and finish line.

The time at the start line is there, it's 7.

22 seconds, and the time at the finish line is there, it's 7.

31 seconds.

So pause the video, work out the time it took to pass between the two lines and then restart and we'll see the answer.

Okay, the answer to that was 0.

9 seconds.

And you get that by subtracting the start time from the finish time, 7.

31 minus 7.

22.

It's 0.

9 seconds.

Well done again if you've got that.

Okay, the final task of the lesson is a practical one.

I'm gonna ask you to time how long it takes a little animated car to move between the start and finish lines shown on this slide.

I'm gonna make that car travel between three times and I want you to measure the time three times.

You'll need some sort of electronic timer to do this.

So if you haven't got one, get one handy now.

I'll announce when I'm gonna make the car move, but you should watch carefully and try and observe it pass the start line and pass the finish line and write the values down and then calculate an average speed.

Okay, let's have a look with the first run.

Okay, let's have a look at the first run.

This is run one, so observe carefully and time this car.

And now it's time for the second run.

So watch carefully again and measure the time it takes the car to move between the two lines.

And here's the third run.

Again, one final measurement.

Measure how long it takes the car to travel between the start and finish line.

Okay, your results should look something like this, but different computers will run that animation at slightly different speeds.

So there will be some variation and obviously there'll be some timing errors that you may have made.

So my results were 1.

34, 1.

31 and 1.

37 seconds.

And I calculate the mean by adding those three values together and then dividing by three, which gives me an answer 1.

34.

So my mean time was 1.

34 seconds.

Now your results will be slightly different.

I'd like you to think about what you could have done during the experiment to make each one more accurate.

Okay, we've reached the end of the lesson and in this lesson you've learned that the instantaneous speed.

Right now we've reached the end of the lesson and we've got a quick summary slide.

You should have learned that the instantaneous speed of an object is the speed at a particular moment in a journey, how fast you're going at a very specific time.

That instantaneous speed will change throughout the journey.

The instantaneous speed can be estimated from distance divided by time if you measure over a very short distance, so for a very short period of time as well.

Instantaneous speed is shown by a device like a speedometer in a car.

In any timing, there'll be some timing errors and that will be caused by starting or stopping a timer a little bit too fast or a little bit too slowly.

You can reduce those by careful observation and a good method in your practical and practice.

The timing errors are due to random errors and it's impossible to predict if the next measurement will be too big or too small and there's a random error.

But, again, with repeated measurements, you can eliminate some of those problems.

So well done in reaching the end of the lesson and I hope to see you in the next one.

Bye.