Hello there.

My name is Mr. Forbes, and welcome to this lesson from the Measuring and Calculating Motion Unit.

This lesson is called Measuring Instantaneous Speed Analysis, and in it we're gonna analyse a set of results we collected during an experiment to try and measure the instantaneous speed of a dynamic trolley rolling down a ramp.

By the end of this lesson, you're going to be able to explain how to accurately measure instantaneous speed of an object, and produce reproducible and repeatable results.

You're also going to be able to make suggestions about how to improve the experiment, and how you can analyse the behaviour of the trolley to see if there's a pattern there.

The key words you'll need to understand for this lesson are here.

They are repeatable, and repeatable means that the results are the same each time you carry the experiment out yourself.

Reproducible is the second, and that means the results of the experiment are the same when other people carry out your method.

Third is instantaneous speed, that's the speed of an object moving at one particular moment in time.

And then directly proportional.

Variables are directly proportional if one is a constant multiple of the other.

And here's a set of explanations for those keywords that you can return to at any point during the lesson.

The lessons in three parts, and in the first part, we're gonna look at the meaning of repeatable and reproducible, and how we get measurements that are repeatable and reproducible by making sure that our method is detailed and gives all the instructions required.

In the second part, we're going to take a set of data and analyse it to see if there's any pattern in the result, by seeing if one thing is directly proportional to any other.

And in the third part, we'll look at ways of improving the measurement and the accuracy of our instantaneous speed measurement.

So let's get started by looking at repeatable and reproducible measurements.

Okay, the words repeatable and reproducible are used to describe the sets of results we get in an experiment.

They're very similar and very easy to confuse, so we've got to be very careful with our definitions of them.

So repeatable results mean that the method is repeatable if it gives the same or very similar results when the instructions are followed by the same person several times.

So they carry out an experiment, get a set of results, carry out the experiment following the same method, and get a very, very similar set of results.

Reproducible is a little bit different in that the people who are carry out the method are a different team of people.

So if a different team of people take your set of instructions, follow them, collect data, that data is very, very similar to the original data that you collected.

So repeatable means that it can be repeated by you, and reproducible means it's done by somebody else, a different team or person.

Let's check if you those definitions here.

So Andeep carries out an experiment three times and gets the same result each time.

He shares the method with Sofia and she gets a different result.

So I'd like you to decide about repeatability and reproducibility.

So is the method was not repeatable and not reproducible? Is it that the method was repeatable but not reproducible, the method was reproducible but not repeatable, or finally the method was reproducible and repeatable? So be very careful with the definitions of those words.

Pause the video, make your decision, and then restart.

Okay, welcome back.

The correct option here was the method was repeatable, because Andeep could do the experiment several times and get the same results each time, so that's repeatability, but it's not reproducible.

Sofia couldn't get the same result when she tried to carry out the same method.

So the answer is B.

Well done if you got that.

In order to get a set of reproducible measurements, what you need to do is to write a method that's good enough that another person can take it from you, read through it, follow the instructions, and get exactly the same set of results as you've got.

So they need all the details to be present there.

So the details you'll need to include in your method would be, you've got to be very, very specific about the key measurements used to set up the equipment.

So how high is an object supposed to be? What distance is there supposed to be between certain markers? How long is something gonna go on for? How many results are you gonna collect? So key measurements need to be described in quite a bit of detail.

A diagram showing where the measurements are taken from can make that much easier.

So if you're measuring the height of something, give a labelled diagram that shows where the height is.

It's the height between one object and another, where exactly you're measuring from and to.

You need clear ranges for the independent variables, so how many different sets of measurements you're gonna take.

If you're increasing the height of a ramp, how many different heights you're gonna use, and what precisely are those heights? So is it one centimetre, two centimetre, and three centimetres, or is it every half centimetre? So give as much detail about the independent variable as you can.

You should provide some way of recording those results.

It'll make it easier for the other team to record precisely what you mean.

And finally, we should describe how you're controlling all the control variables, as much detail as necessary.

So which things are you keeping the same, and how are you making sure they stay the same between each test run? So I'm going to show you an example of a method that seems okay at first, but it's quite poor.

It doesn't contain enough details.

So let's start by looking at the diagram.

We've got the diagram here, and this looks fairly okay.

It's got a set of books holding up end of the ramp.

It's got a trolley on it, it's got some straws marked on, so it's labelling the parts.

So it kind of shows how things are set up.

There's not much detail on it.

The instructions here say, "Start with one book." It's a bit vague, but we'll continue from there.

Then it says, "Roll the trolley down the ramp and measure the time it takes to travel between the two markers." Well, that's okay.

The trolley's gonna roll down the ramp.

It's gonna pass between two markers, and they're recording the time and the number of books used.

The roll is a bit misleading.

Does that mean you push it or just release it? So it's a little bit vague.

Repeat the test two more times on the same ramp, record the times.

That seems reasonable.

Add another book and repeat the tests.

Use more books to give more sets of results.

So you can probably follow that set of instructions and collect some sort of results, but it doesn't contain any detail about how to precisely do that to get accurate results.

Let's have a look at some ways of improving this method.

So as we read through, the first thing that I notice is it talks about numbers of books.

It would be much better if we didn't just say books, because that's a bit vague.

How thick is one book? Are they all identical books with the same thickness? It would be better if we precisely measured the height of the ramp at that end.

So I would change this method to talk about measuring the height for each test run.

The distances between the two markers isn't specified.

If I followed this set of instructions, it would, you know, I'd place them at small distance, but that might be five centimetres, it might be 10 or it might be 20 centimetres.

I need to precisely specify what distance that is.

And I need to also make sure I start the trolley at the same start point for each test run.

So releasing it from the same point is quite important, otherwise the start height would be different each time.

It wouldn't match the measurements I've made for start height.

So there's some possible improvements for that method.

Okay, let's check if you understand why it's important to write out a detailed method.

So which of these are important to make sure a method is reproducible by other teams? Is it A, there should be as many tests as possible in the time available? Is it B, the range of values for the independent variables should be given? Is it C, the instructions should be a series of neat bullet points? Or is it D, how to take measurements should be clearly explained? So pause the video, make your selection, and then restart.

Okay, welcome back.

The two options you should have chosen are these.

First of all, the range of values for the independent variable need to be specified.

I need to know how many different heights I'm using and precisely what those heights are, otherwise, whoever's doing the experiment the next time might use different heights, and I'll get different results.

Then how to take the measurement should be specified as well.

So I need a clear explanation of how I'm going to get the timing measurements for the trolley rolling down, and where I'm gonna measure heights from.

The other two options are possibly useful, but they're not essential to get a reproducible set of results.

As we saw the method that we started with originally could give a range of differences in the results for the tests.

So I've got two groups here.

They both tried to follow the original set of instructions, and as you can see, the first thing they've done is they've used different thicknesses of books.

So when one group says one book, it's going to be taller than the other group that's used a thinner book.

So they don't match up very well.

The books are at different heights, and we should have specified the heights instead of just number of books.

The second thing that wasn't specified was the small distances at the end.

One group could use 10 centimetres for the distance, and the other 20 centimetres.

And obviously those values for timing is gonna be very, very different as the trolley passes between the two of those, so we're gonna get a different set of results entirely.

The data that we get at the end of an experiment will tell us if the method was reproducible or not.

So if we compare the results from different groups trying to follow the same method and they get the same type of data, the same patterns, and it's reproducible, otherwise perhaps it's not.

So we're gonna look at three sets of data to see if the method was reproducible.

We've got a set of data here.

So group A has collected this set of timings for different heights, group B, this set of timings and group C.

And what we do to check if the method was reproducible is look across, and we'll start with start height one centimetre and compare the results for the three separate groups.

And as you can see here, they're all pretty close together, so that suggests this was reproducible.

Looking at the start height of two centimetres, again, we've got a set of results that match each other very closely.

And finally, the third one, they also match.

So I'd say that whatever method was used here was very reproducible.

I'd like you to look at these three sets of data collected by three separate groups, and decide whether they're repeatable and reproducible.

So they're repeatable, not repeatable, reproducible or not reproducible.

I'd like you to choose the two correct answers, please.

Look carefully.

Pause the video and restart.

Okay, welcome back.

These results are repeatable.

If you look across for each group, say group A, height one centimetres, the three values for the time are very similar.

If you do the same for each group and each height, you'll see that they're getting similar results each time.

So they're repeatable by each group, but they're not reproducible.

Each group's data is very different than other group's data.

So there's clearly something in the method that's not being specified properly to make these reproducible results.

Well done if you've got those two answers.

Okay, time for the first task now, and what I'd like you to do is to read through this method and try and write out an improved version of it, so that you might get more reproducible results.

So pause the video, rewrite the method, and then restart.

Okay, welcome back.

And the main thing I've done to improve this method is specify the start heights and the distance between the two markers.

So by specifying that, each group will know how far apart to put the markers and how far, sorry, how high they should release the trolley from.

The rest of the method has only got minor improvements where I'm specifying that I'm recording the time precisely for different heights, instead of numbers of books.

And I'm also describing how many times I'm going to do the experiment, and how many sets of results I'm aiming to get by the end.

So well done if your method looks something like this.

Now it's time for the second part of the lesson, and in this we're going to look at the data that's collected and see if we can find a pattern in it, see if it matches any predictions we may have made.

So we're gonna analyse the speed patterns.

We can use the results of the experiment to look for patterns in it, and sometimes those patterns are obvious and they match simple predictions, and we can tell that very easily.

So I've got a set of results here.

Let's say our prediction was the speed of the trolley increases when the ramp is steeper.

Well, we can check if that is right by just looking at the patterning in steepness.

So there's the increasing steepness of the ramp, and then comparing it to the instantaneous speed there, and we can see the steeper the ramp, the more the speed increases, so it's faster for a steep ramp.

And that shows that that prediction was correct.

So a simple prediction like that is quite easy to check just by looking at the data on the table.

Not all predictions are as easy to check.

If we've got a more complicated or mathematical prediction, then we need to do a bit more analysis.

So I've got the same set of data here, but this time I've got a mathematical prediction, a prediction about direct proportionality.

The instantaneous speed of the trolley is directly proportional to the ramp height.

Now, two variables are directly proportional to each other if one is always a fixed multiple of another.

And it's not always easy to see that just by looking at results in a table like this.

The best way of finding out if a pair of variables are in direct proportion to each other is to plot a graph.

So I would get a set of graph paper, and I would label up some axes like this.

So I'm testing if ramp height and speed are directly proportional to each other.

And I would plot my data on that graph and I'd draw a line of best fit through them.

Now, if those two variables were in direct proportion, there'd need to be two things about that line.

First of all, it needs to be straight.

So a straight line of best fit.

And second, a line of best fit must pass through the origin.

So if this was my set of results and I'd plotted them accurately, then I would be able to say that the speed is in direct proportion to the ramp height.

Let's check if you understand that.

I've got three graphs here between variables.

Variables are just called X and Y here.

It doesn't really matter what they are.

But which of those graphs shows direct proportionality? Which one shows that X is directly proportional to Y? Pause the video, make your selection and restart.

Okay, welcome back.

You should have chosen graph C.

Graph C is a straight line and it passes through the origin.

It wasn't B because that's a curve line, and it wasn't A because that line does not pass through the origin.

So well done if you selected C.

Okay, in a little while I'm gonna ask you to plot a graph using the data that I'll provide.

Here's the steps just to make sure you remember all the key stages.

So I've got a set of data here.

What I should do is draw the x and y-axes on that graph paper.

So I'll draw them there.

Then I'm gonna add the two different scales.

I've got my scale on the bottom here, and I've got my vertical scale here.

And those two scales, remember, don't have to be the same as each other.

If you go one to six on one, you don't have to go one to six on the other scale.

Next, add some axes labels.

So this is the ramp height and this is the speed.

And then I start to plot the data.

So each time I'm gonna plot one simple cross, not a big blurry one, as precisely as I can from that table.

And I like to tick off each value as I've done it, so that I don't mess them up.

So first of all, plotting the first one, second and so on until I've plotted all of the data.

So now I've got my points plotted on the graph.

So the next thing I should do is try and add a line of best fit to my series of points.

There's two types of lines of best fit.

The first is either a single straight line that passes through the points or very close to them.

So I can only draw a straight line with a ruler.

So I get out a ruler, and I try and put it through those points to see if they fit.

I can adjust the angle of the ruler, until eventually I find what I feel is the best line of best fit that goes closest to the points, with some above and some below.

But if the points don't seem to go along that line, I shouldn't draw it.

So I've got two potential line of best fits here, and the red line is reasonably close, but I don't think that those points are exactly on a straight line, and the green line certainly isn't a good line.

I tried to force it through zero there to see if it was directly proportional and it certainly isn't.

So I'm gonna abandon that straight line of best fit.

And what I'm gonna do is try and draw a smooth curve passing through the points.

So drawing a curve, something like this close to the points, kind of shows them on a curved path rather than a straight line.

So I would say that if this is the line of best fit, then these two things, ramp height and speed and not in direct proportion to each other.

I've got a set of data here and I've attempted four different lines of best fit, two of them curves and two of them straight.

I'd like you to look at the points carefully and the lines, and decide which of the lines label A to D there is the best line of best fit.

So which one is the most appropriate one to draw? So pause the video, make your selection, and then restart.

Okay, welcome back.

You should have selected line A.

Although the graph is quite crowded and it can be difficult to see, A is the line of best fit that I should have drawn on this one.

So line A, the yellow one, and it's a single smooth curve and it goes close to the points without being forced to go through them.

The straight lines don't fit the points at all.

And line C, the wibbly wobbly red dotted line is kind of forced through the points.

So it's not a single smooth curve, it's a series of curves in different directions, so it's not appropriate.

Well done if you chose line A.

Okay, time for the second task of the lesson now, and the task is for you to use this data to plot a graph.

So I'd like you to plot a graph showing the relationship between ramp height and average speed using the data in that table.

Once you've plotted that graph, I'd like you to think carefully and then draw a line of best fit.

And once you've drawn your line of best fit, I'd like you to write a conclusion based upon the line that you've drawn.

So pause the video, try those three parts of the task and then restart, please.

Welcome back.

I've plotted the graph here, and as you can see I've drawn a line of best fit and I've chosen to draw a curve.

I don't feel that all the points lie on a straight line that passes through the origin, so I decided that a curve seems to be the best fit for these.

And my conclusion based upon that is the instantaneous speed is not directly proportional to the height of the ramp.

So the speed isn't directly proportional because it's not a straight line that passes through the origin.

Well done if you've got those.

Now it's time to move on to the final part of the lesson, and in it, we're gonna look at a couple of ideas about how to improve the accuracy of our measurement of instantaneous speed.

So let's start with that.

To calculate our instantaneous speeds, what we've actually been doing is measuring an average speed for a short distance and a short period of time, and that gives the estimate for the instantaneous speed.

To get a better estimate, you might think, well, we could use a smaller distance and a smaller time, and that will give a more accurate version.

So perhaps a distance of 10 centimetres instead of 20 centimetres could give us a more accurate value for the speed.

But would the time be hard to measure if we've got a very small distance and the trolley's moving through it? I'm trying to measure the time with a stopwatch manually, and I might have to take into account reaction time.

So let's have a look at an example speed and see what typical times it might be.

I've got two straws here placed 10 centimetres apart, and I'd like you to work out how long it would take for a trolley travelling at one metre per second, so not particularly fast, to travel those 10 centimetres.

So pause the video, calculate the time, and then restart.

Okay, welcome back.

And you should have calculated 0.

1 second.

If you see the maths here, we've got T equals 0.

1 metres, that's 10 centimetres divided by one metre per second, gives us a time of 9.

1 seconds.

Well done if you got that.

And now I'd like to see if you can remember what typical reaction time is once you've practised making a measurement.

So which of those would be a typical reaction time for an experiment like this? Pause the video and then restart when you've decided.

Okay, well, typical reaction time after you've practised a bit is about a 10th of a second, so 0.

1 seconds.

Well done if you got that.

We can use those two ideas to see if using 10 centimetres is a sensible improvement to the experiment.

So if I've got errors in the timing value, that'll give me an inaccurate value for the speed.

Now, a trolley moving at one metres per second would take 0.

1 seconds to pass between the two straws.

But if my reaction time was added to that, so I've got a reaction time of 0.

1 second, I might actually measure time of 0.

2 seconds with that reaction time included.

And when I calculate the speed based upon that, instead of the true speed of one metre per second, I'd actually end up finding that the speed is 9.

5 metres per second, so only half of its true value.

So having that small distance doesn't seem to have improved the experiment.

So let's have a look at an alternative way of trying to improve the experiment, and that is to make the ramp more shallow, a less steep gradient.

And what that will do is slow down the trolley, and hopefully I'll be able to measure the timing more accurately as it moves between the two markers.

But if I make the slope too shallow, perhaps the trolley won't be able to accelerate enough at all.

I've got a trolley on the ramp here, and there's gonna be a force on a trolley accelerating, so it rolls down the ramp.

But which force tries to slow the trolley as it moved? Is it the gravitational force on the trolley? Is it frictional force? Is it the weight of the trolley? Or is it the normal reaction force from the ramp? So pause the video, make your selection and restart.

Welcome back.

You should have chosen frictional force.

So frictional force, that's going to slow it down.

Now, a dynamics trolley has a very small frictional force, so it might not be that significant, but that's the force you should have chosen.

Well done for selecting that.

Even though the frictional force acting on the trolley is very small because of the way it's designed, if it's large enough then the trolley won't roll.

So if I've got a ramp and I've got a force pulling the trolley down the ramp that's larger than the frictional force, the trolley's going to accelerate and it's gonna move between the two markers.

But if that force pulling it down the ramp isn't large enough because the gradient isn't high enough, then the trolley's not going to accelerate, and it's not going to roll down the ramp and go through those two markers.

By carrying out some test runs testing different heights that I start the trolley from, then I can try and judge which one's going to get me the best, easiest to measure speed that the trolley's moving between the two markers.

So test runs are always a good idea in an experiment like this.

Another issue with this experiment is actually where you're going to take your measurements from, because you're looking at two separate markers along the track, and it's difficult to position yourself so you can see exactly when the trolley reaches each of those markers.

So if you position yourself in line with the first marker, then you can see the trolley past that, but you can't really see it pass the second marker very precisely.

And if you position yourself at the other marker, so positioned there, then you can't see it past the first marker clearly.

So it can be very difficult to position your eyes properly.

The best position to position yourself is probably somewhere in between.

So you're gonna get some error measuring it go through the first marker, and you're gonna get some error measuring it go through the second marker.

But those two errors, because you're looking from different sides, will probably cancel each other out, and you'll get a fairly accurate measurement of when it passes the markers.

Let's see if you can choose an appropriate position for an experiment.

So I've got a ball, dropped it, and it's passing by that marker, and I've drawn it in that big blue arrow, and I'd like you to decide where would you position your eye to see that ball pass that marker, is it in position A, B, C, or D? So pause the video, select the position, and then restart.

Okay, welcome back.

You should have chosen C.

That one is not perfectly in line with the marker, but it's the closest to it, and it's gonna give you a fairly accurate idea of when the ball is past the marker.

So I'm observing from the top of the ball there.

If I look from the other positions, such as up here, then the ball would be there, where I put that dotted circle, and that's quite far away from the marker.

From B, it's a bit closer, but it's not as good as point C.

And from D, well, the ball would've passed the marker by quite a fair distance there, so that's not very good.

So well done if you chose C.

Okay, we're at the final task of the lesson now, and I'd like to check that you've understood all of the concepts that we've covered.

So I've got a feather here, and I'm gonna drop it from a height of one metre.

I'd like you to write a method that would allow the instantaneous speed to be measured as that feather reaches the ground.

And then I'd like you to discuss reasons why a feather is a good or a bad choice for this type of dropping experiment.

So pause the video, write that method and discuss the reasons and then restart.

Okay, welcome back.

And here's the sorts of things I would expect in a method.

You'd be measuring a small distance 'cause you want to try and find instantaneous speed, so 20 centimetres or 10 centimetres.

Trying some test runs to see which distance of those works best.

Marking the distance so you can see further past those two points, so things like drawing a line on a wall.

Observing very carefully, and that's tricky in this experiment.

You need to get your head close to the floor, or perhaps put some sort of video recording equipment, so you can see the feather moving.

Repeating the measurements and getting a meantime, and then calculating the speed using the relationship there, speed is distance divided by time.

Well done if you've got a method that looks anything like this.

And the advantages and disadvantages are discussed here.

The advantages include things like the feather's gonna fall slowly, so it's going to be easy to measure its speed.

It's not going to be moving very fast.

And the disadvantages, well, the feather's gonna be rocking from side to side as it falls through the air, so that's going to be difficult to position all your equipment to measure precisely.

Its shape isn't uniform, so it's very difficult to decide exactly which part of the feather you're measuring from and to, because it might fall different ways during different tests.

So well done if you spotted those advantages and disadvantages.

It's nearly the end of the lesson now, so here's a quick summary of everything we've gone through.

So a method is repeatable if it gives the same or very similar results when the instructions are followed by the same person.

So you can repeat your own experiment.

It's reproducible if it gives the same or similar results when they're followed by a different team, so somebody else reproduces your results.

The accuracy of an instantaneous speed measurement depends on how accurately you measure the time and the distance measurements, and that's affected by reaction time and observation position.

When you analyse data, you might see it's in direct proportion, and you get a graph like that one there, where the line is straight and it passes through the origin.

So well done for reaching the end of the lesson.

I'll see you in the next one.