Hello there.

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

This lesson's measuring instantaneous speed and in it we're gonna be carrying out an experiment to try and measure the instantaneous speed of a dynamics trolley as it rolls down a ramp.

In this lesson, I'm going to be explaining how you can carry out an experiment to measure the instantaneous speed of a dynamics trolley, a small, wheeled trolley that we'll put on a ramp, and we'll try and measure how long it takes for it to travel a very small distance and use that distance and time information to calculate an instantaneous speed.

The key words and phrases you need to understand to help you understand the lesson are shown here.

The first is average speed, and that's the total distance travelled divided by their time taken for a journey.

Instantaneous speed, is the speed at a particular moment in time.

A dynamics trolley is just a wheeled trolley we use in quite a wide range of experiments of motion.

And an anomalous reading is a reading that's out of a path in some way.

It's generally an incorrect or wrong reading.

And here are the explanations for those key words.

You can return to this slide at any point during the lesson.

The lesson's in just two parts, and in the first part we're going to be planning and then carrying out the experiment into measuring the instantaneous speed of that dynamics trolley.

And in the second part, we're gonna take the data we've collected, we're gonna process it by removing any anomalous results and then try and get an accurate value for the instantaneous speed.

So when you're ready, let's start planning.

For this experiment, we're gonna need to use the speed equation, or the average speed equation, and that's this equation here, speed equals distance divided by time.

We often write that in symbols as V equals S divided by T.

Those symbols are defined here.

Speed, V, is measured in metres per second, distance travelled, we use the letter S for that and that's measured in metres, and time, T, is measured in seconds.

When an object's moving, it's not usually moving at a constant speed.

It's instantaneous speed is changing quite often, and so the average speed and the instantaneous speed are not the same thing.

If I've got a sprinter running along the track, it's a hundred metre track, and they take 10 seconds to run that race, they'll have an average speed of 10 metres per second, but near the start of the race, they're gonna be starting from the speed of zero and speeding up.

So their instantaneous speed in the first section of the race might be quite low, but their instantaneous speed near the end of the race, as they're approaching the finish line, will be much higher.

To measure the instantaneous speed of something, what we do is we actually measure the average speed for a very small section of the journey.

So for a very small time period, or a very small distance.

So for the sprinter earlier, what I could do is measure the average speed, for just a one metre section of the race.

So here's a one metre section of the race near the beginning, and it takes a sprinter 0.

25 seconds to travel that one metre.

So it can calculate the average speed here, it's four metres per second, and that's very close to the instantaneous speed for that section of the race.

Later on in the race, near the end, the sprinter travels one metre in 0.

08 seconds.

They're travelling much faster there, so I get an instantaneous speed of 12.

5 metres per second.

Let's check if you understood that.

Is this true or false? Instantaneous speed can be found by timing the movement through a large distance.

So pause video, make your selection and restart.

Welcome back, well, that one was false.

I'd like you to justify the answer you chose there.

So choose one of these two.

Any speed changes would be smaller within a short distance, or it's not possible to change speed within a short distance.

Pause video, select one of those and then restart.

Okay, the answer to that one was the top answer.

Any speed change would be smaller within a short distance.

You couldn't speed up much, or slow down much, within that short distance in time.

So the instantaneous speed is best measured in a short distance on a short time.

So the experiment we're gonna carry out involves a dynamics trolley rolling down a ramp, and we're going to try to measure the instantaneous speed of that trolley.

So the trolley's going to speed up as it moves down the ramp because there's gonna be force acting on it, and that resultant force is going to be greater than any frictional force slowing the trolley.

So as the trolley's on the ramp, it's going to speed up as it rolls towards the bottom, its instantaneous speed is gonna be changing, because it's getting faster and faster, and it's gonna be highest towards the bottom of the ramp.

We can change the force acting on the trolley by changing the angle of the ramp.

So if I get a ramp and lift it up a little bit, perhaps by placing one book underneath one end, then there's gonna be a forward force and that's gonna make the trolley roll down.

If I put two books, there's gonna be a greater forward force acting on it and that's going to make the trolley go faster and faster.

And if I put four books, then there's gonna be quite a large forward force acting on it, so it's gonna go faster again.

So the instantaneous speed of the trolley is going to be greater at the end.

A check of your understanding of how the trolley's gonna move now.

So I've got a result force acting on a trolley as it travels down a ramp, which of the following are true? Is it, the trolley moves at a constant speed, the trolley will be accelerating as it travels, the instantaneous speed at Y is greater than the instantaneous speed at Z, or, the instantaneous speed will be greatest at Z? So I'd like you to choose all of the correct options please.

Pause the video and then restart.

Welcome back.

Well, you should have chosen these options.

The trolley will be accelerating as it travels, so it's getting faster as it moves down the ramp.

And the instantaneous speed will be greatest at the end of the ramp Z.

So well done if you've got those two.

So the investigation you're gonna carry out today is to find out how the steepness of the ramp affects the instantaneous speed of the trolley at the bottom.

So we're gonna vary the steepness of the ramp and measure the instantaneous speed for different steepness.

So we're gonna place the trolley on a ramp like this.

We're gonna control the start height.

So the height is the thing we're gonna alter.

And what we're gonna do to measure the instantaneous speed is to measure how long it takes the trolley to pass between two markers.

And those markers are gonna be placed where the trolley's gonna be fastest at the end of the ramp.

We're gonna place them a small distance apart and we're gonna use a distance where we can effectively measure the time with the start watch.

So we're gonna place them about 20 centimetres apart there.

Okay, let's check if you understand the type of variables involved in this experiment.

So what I'd like you to do is to match the variable to the variable type by drawing lines.

So we've got three variable types, dependent, independent and control, and I've got four different variables there.

So obviously because there's more variables and variable types, two of them are gonna be the same, and those two are the control variables.

So pause the video, connect the variable types to the variables with lines, and then restart.

Okay, welcome back.

Well, the first of these is the dependent variable, and that's the thing that we're measuring, the sort of output of the experiment.

We're gonna be measuring the instantaneous speed of the trolley.

The independent variable is the thing we change during the experiment to see how it affects the output.

So the independent variable here is the height of the slope.

And the two control variables, one's the mass of the trolley, we should use the same trolley each time.

And the second one is the distance between the two markers at the end of the ramp.

So well done if you've got all of those.

Okay, now it's time for you to carry out the experiment.

What I'd like you to do is to set up the equipment as shown in the diagram here.

Yours might be very slightly different because you might use a different method for raising the end of the trolley.

I've used a set of books of equal thickness in this one, but you might have a different system.

You are gonna place the trolley at that release point, release it and allow it to roll, and time how long it takes to go through the gap between those two markers that are placed on the ramp.

So you set up the equipment, you measure and record the start height, then you release the trolley so it rolls on the ramp, and measure the time it takes to travel between those two markers.

Now it's gonna be moving fairly slowly for you to be able to record a sensible time there.

You're gonna repeat that test twice more on the same ramp, recording the time.

So you've got a set of three there, three timings.

Then you're gonna increase the gradient by adding another book or raising up by some other method and repeat the process, getting three more times for a different gradient.

And you're gonna increase the gradient a few more times until you've got five different gradients, five different steepness of the ramp.

So I'm gonna show you a video of that process being carried out so you can get a better idea.

<v Narrator>In this demonstration,</v> we're going to measure the instantaneous speed of a dynamics trolley at the end of this slope.

We've set up two lollipop sticks at the end to mark a 20 centimetre length.

And we're measuring the trolley as it goes down one metre of the track, we've put the one metre in the centre of the two lollipop sticks, so that we're measuring the speed in the centre of them.

If you like, we're measuring the average speed over that 20 centimetre length and the centre point is right in the centre of the length there.

So that's going to be the average speed at that point halfway along.

Now you could use a stopwatch, to actually start and stop the stopwatch as it goes past the firstly pop stick.

And then after the second one.

Instead what we're going to do is going to video the trolley going past the two lollipop sticks and pause the video each time to take your reading off the timer.

So here's the first measurement coming up, as the trolley just comes down the slope.

(wheels rolling) And here's the second measurement.

(wheels rolling) And the third measurement for the same slope.

(wheels rolling) And now three more measurements for a steeper slope.

(wheels rolling) And then three more measurements for an even steeper slope.

(wheels rolling) You'll have noticed that some of these measurements were really hard to take, even with the video recording being frozen.

It might be worthwhile just going back and looking at those measurements again, and to have a think about how accurate they actually are.

<v ->And after you've seen the video,</v> hopefully you've got everything you need to carry out the experiment.

So pause the video, carry it out, and collect a set of results for me.

Okay, welcome back.

Hopefully your experiment went well and you've got a set of results something like this.

I've got five different start heights, each one centimetre, and I've got a set of timings for each of those.

So I've filled in most of the results table for that.

I've got some space for some calculations we're gonna be doing in the second part of the lesson, but you shouldn't have filled those in yet.

So your results should look similar to that sort of pattern, but they won't be the same.

Well done if you've got that done.

So we've carried out our experiment and we've got a set of data.

So what we need to do now is to process that data to try and find the best value for the instantaneous speed of the dynamics trolley.

So let's get doing that.

In any set of results that we collect, there are often values that don't fit the pattern.

They're clearly different than the other sets of results for those repeated tests.

Those type of results are called anomalous readings.

And I've got one here.

If you look at ramp height, one centimetre, you see you've got three values.

Two of those values are very close together, not 0.

42 seconds and not 0.

41 seconds, but one is quite far apart, so that anomalous reading doesn't fit the pattern.

What I should do in that case, 'cause I've probably made some sort of timing error in the experiment, is I should try and repeat the experiment.

So I should cross it out and repeat that experiment if possible.

So I've done that here.

It's not always possible to repeat an experiment, because you've not got time, or you've put the equipment away and you hadn't noticed that you've got anomalous results.

So in that case, what you should do is just cross it out and ignore it.

Don't use that value in any calculations or any graph work later on.

Okay, let's see if you can spot anomalous readings.

I've got a complete table of data here and there's one anomalous reading in there.

I'd like you to spot that anonymous reading and identify it clearly please.

So pause the video and restart once you've spotted the anomalous result.

Okay, welcome back.

Hopefully you spotted the anomalous result was here, the height three centimetres, the second time reading, that's significantly different than the other two values.

All the other values in the table look okay to me.

The reason you collected a series of times for the same ramp start height is so that you could calculate a mean time.

What a mean time does is eliminate some of the random error where your values are slightly too high or slightly too low.

So we're going to show you how to calculate a mean time.

So the mean is the sum of the results divided by the number of results there are.

So for height one centimetre high, find the mean by adding the three results and then divide it by three.

And that gives me a mean time of not 0.

44 seconds.

I can do the same process for height two centimetres, gives me a different mean time, and then I can do the same process again for the height three centimetres.

So I'm adding the values together and dividing by how many values there are.

So I'd like you to find the meantime for this set of readings, but look very carefully at the readings before calculating that meantime for me.

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

Okay, welcome back.

Hopefully you've got a value of not 0.

45 seconds.

And the reason for that is we need to cross out the anomalous result first.

That result clearly doesn't fit the pattern.

It's too high.

So I've crossed it out.

Now I've got three readings.

So I calculate the meantime by adding those three readings and dividing by three, given me a meantime of not 0.

45 seconds.

Well done if you've got that.

Now I've got the mean times that it took the trolley to move between the markers for each of the different ramp start heights I can calculate the instantaneous speeds.

So the trolley travelled not 0.

2 metres, 20 centimetres between the markers.

So for ramp height one, I can write out the equation to calculate instantaneous speed like this, and I can identify the values as my meantime, and there's my distance, and substitute those in and that'll give me an instantaneous speed of 0.

45 metres per second.

I can repeat the process for a second set of data and that'll give you a different instantaneous speed.

And I continue down the table, until I've got all instantaneous speeds.

Okay, it's time for you to analyse your data.

So what I need you to do is to calculate the mean times for your set of data, and then use those mean times to calculate the instantaneous speeds.

If you don't have any suitable results, then you can use the data I've got on the table here.

So pause the video, calculate your mean times and your instantaneous speeds, and then restart when you're done.

Okay, welcome back.

Your table should now look something like this.

As you see in my table, I add two anomalous results, I've crossed them out.

I've calculated the mean times for all of the values, and from those mean times I then calculated the instantaneous speed.

So I've got instantaneous speed there in the end column, and that looks like it's increasing as the ramps height increased, which is what I expect to happen.

Well done if you've got something like this.

So we're at the end of the lesson now, and here's all the information you should have learned during the lesson.

The instantaneous speed of the dynamics trolley can be found by measuring the time it takes to travel through a small distance.

And I used not 0.

2 metres there.

We calculated the speed using the equation, V equals S divided by T.

And we learned that we needed to cross out anomalous results, replace them with new readings if possible, or ignore them in any calculations if it wasn't possible to do that.

So well done on reaching the end of the lesson.

Hopefully I'll see you in the next one.