Lesson video

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

In the lesson we're gonna be looking at changes in velocity and using those to find the acceleration of moving objects.

By the end of this lesson, you're going to be able to find the change in velocity of an object and use that change in velocity and time measurements to find the acceleration or deceleration of an object.

And here's a set of keywords that you'll need to use throughout the lesson.

The first of them is velocity.

The velocity of an object is its speed in a particular direction.

The second is rate of change and a rate of change is how much some quantity changes every second.

A third is actually a symbol and it's delta-v and delta-v is used to represent the change in velocity.

And is acceleration and acceleration means an object speeding up or change in direction and deceleration, which we use for slowing down or change in direction.

And this is a set of definitions of 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 going to be looking at changes in velocity.

We've already seen that velocity is speed in a particular direction, but we'll be calculating the changes using two different velocities starting at an end velocity.

In the second part of the lesson, we're going to be using those changes in velocity and time information to find the acceleration of an object, how much faster it's getting per second.

And in the final section we're going to be looking at deceleration, which is when object is slowing down or accelerating backwards.

So when you're ready, let's begin with changes in velocity.

Hopefully you remember that velocity of an object is the change in displacement each second, and we can express that as a simple equation like this.

Velocity is change in displacement divided by time.

When we say that velocity is the rate of change of displacement or how much the displacement of the object changes every second.

So we can see two examples of that here.

We've got a velocity of five metres per second, and what that means is the displacement is changing by five metres every second.

So after two seconds the displacement would've changed by 10 metres or we can have a velocity measured in kilometres an hour like this, two kilometres an hour means the displacement is changing by two kilometres every hour.

So let's practise calculating some velocities.

I've got a question and I'll answer it and then I'll ask you to do one.

A lorry takes four hours to reach a destination 92 kilometres south of the starting point.

Calculate the velocity of the lorry.

So the first thing we should do is write down the equation we saw earlier.

Velocity is displacement divided by time or change in displacement.

We write that down.

Velocity is 92 kilometres divided by four hours.

Identifying those two from the question and finally do the calculation.

It's 23 kilometres per hour and we've got to give a direction as well.

So it's to the south.

Now it's your turn.

I'd like you to calculate the velocity here.

A jogger runs 280 metres in a straight line in a time of 80 seconds.

Calculate their average velocity.

So pause the video, work out your solution and then restart please.

Welcome back.

You should have done your calculation like this.

So first of all, write out the equation, velocity is displacement, divide by time.

Identify those two values in the question.

So the displacement's 280 metres, time was 80 seconds and we then just do the calculation 3.

5 metres per second and we've got to give a direction.

So the only thing we can really put there is along the line in whatever direction they were travelling initially.

Well done if you've got that.

Any object that's speeding up or slowing down has got a velocity change.

And so we've got two values for velocity.

We have the initial velocity, the velocity they started at and the final velocity, the velocity they finished up at.

And the change in velocity can then be calculated from the difference between those two values.

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

I've got a train travelling east six metres per second and it speeds up to nine metres per second still east.

What's the change in velocity? Well, all we need to do is to find the change of velocity, it's final velocity minus initial velocity and it's very important to write it that way around.

We want to take away the starting velocity from the final velocity.

We substitute in the two values.

So the final velocity was nine metres per second and the initial velocity was six metres per second.

So just subtract those and that gives a change in velocity of three metres per second and the velocity's changing in the eastward direction, so we should write that down as well.

Now whenever we're talking about a change in a quantity, we can use the symbol delta to represent the word change instead of having to write out things like initial and final velocity.

So we write that Greek letter delta, which is that triangle symbol you see there.

Examples of that a change in time could be represented by delta for change and T for the time.

A change in displacement can be written as delta-s because we use S for displacement and a change in temperature can be written as delta theta.

So we can use delta to represent any change.

Changes in velocity are known as delta-v because we use V for velocity.

So we use the phrase delta-v for that.

So if a car change its velocity by four metres per second, then delta-v is four metres per second.

Let's try another couple of calculations using that new notation of the delta symbol.

So a skateboarder rolls down a hill in a straight line.

They're travelling at two metres per second at the top and 4.

5 metres per second at the bottom.

Calculate the change in velocity of the skater.

So what they do is I write delta-v to represent change in velocity and it's equal to the final minus the initial velocity.

Substitute those remembering to be careful, the final velocity was 4.

5 metres per second and the initial velocity 2.

0 metres per second.

And I get my answer, it's 2.

5 metres per second.

Now it's your turn.

I want you to use the symbol delta-v in your calculation.

So calculate the change of velocity of the motorcycle here and it speeds up from 3.

2 metres per second to 8.

5 metres per second.

Pause video, work out your solution and then restart.

Welcome back, while using the symbol correctly, delta-v is final velocity matters initial velocity with substitute the two values carefully from the question and that gives us a delta-v, a change in velocity of 5.

3 metres per second.

Well done if you've got that.

So far we've been describing velocities in terms of north, south, up, down, things like that.

But we can also describe it in terms of positive and negative values.

So we're going to be just using positive and negative values for velocity for most of this lesson.

So for example, if movement to the right is shown by five metres per second, then if we want to talk about movement to the left, we can just give a value that's negative.

So minus three metres per second would be a movement to the left.

We need to take those positive and negative values carefully into account whenever we're finding changes in velocity.

And that means that we can end up with changes in velocity that are negative as well as positive.

And we see some examples of that now.

So I'll calculate a change in velocity and then you can have a go.

A stone is thrown into the air at five metres per second.

It's caught when it's moving downwards at minus three metres per second.

So I've got a negative velocity there.

Calculate the change in velocity for the stone.

What I do is I write down the expression delta-v is final velocity minus initial velocity and then carefully identified both of those from the question.

The final velocity was minus three metres per second and the initial velocity was five metres per second.

So that was a positive value.

So I've got a sum there of minus three metres per second, minus five metres per second.

That gives me a change in velocity of minus eight metres per second.

Now it's your go, I'd like you to calculate a change in velocity.

So a ball is thrown at a wall at six metres per second and bounces straight back at minus five metres per second.

Can you calculate the change in velocity of the ball please? So pause the video, do that calculation and restart.

Welcome back, you should have written this delta-v is final velocity minus initial velocity.

And very carefully putting those two values.

We've got a final velocity of minus five metres per second and an initial velocity of six metres per second.

So when we subtract those, we get an answer of 11 metres per second, well done if you've got that.

It's time for a quick check to see if you can calculate velocities.

I've got a car driving up a hill at three metres per second.

It stalls and rolls down the hill at four metres per second.

What's the change in velocity of that car if we take up as being the positive direction? So pause the video, work out your answer and then restart please.

Welcome back.

You should have found a solution of minus seven metres per second.

If we put that in mathematics delta-v is final velocity minus initial velocity, substitute those two values being very careful to take into account direction, it gives a change in velocity of minus seven metres per second.

Well done if you've got that.

Now it's time for the first task.

What I'd like you to do is to complete this table.

The table shows the velocity of three runners as they entered the last section of a race.

It shows the time it took the runners to complete those final 20 metres of the race.

I'd like you to complete that table to show the final velocity, the average velocity over those last 20 metres and the change in velocity please.

So pause the video, work out all those values and then restart.

Welcome back.

Your completed table should look something like this.

The maths behind each of those calculations is shown here so that you can check how you got your results.

Well done if you've got all of those.

Now it's time to move on to the second part of the lesson and we're going to look at acceleration.

We're gonna see how we can use change in velocity to calculate the acceleration of an object.

If the velocity of an object is changing, we say that that object is accelerating and there's two types of acceleration we can look at.

We can look at acceleration based on changes in speed.

The speed can be increasing or decreasing and that will cause the object to be accelerating.

So if a car speeding up say from six metres per second to nine metres per second, that car can be described as accelerating.

We can also have acceleration if the direction of travel changes.

So acceleration of a car turning a corner at constant speed is still acceleration even though the speed stays the same, the direction of travel has changed.

In this lesson we're just going to be looking at objects moving in straight lines that are speeding up and slowing down.

So let's check if you understand what I mean by acceleration.

Which of these statements best describes the acceleration of the train on in the figure? As you can see there's a train and it remains stationary at a station.

So is it the train is accelerating to the right, the train is accelerating to the left, the train is not accelerating or the train might be accelerating or might not be accelerating to the left or right.

We just can't work it out from the diagram.

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

Welcome back.

Well the train's stationary so it's speed's not changing and its direction's not changing.

So the train is not accelerating.

Well done if you chose that.

Before we go on to calculating acceleration, it's important to know that acceleration is a vector quantity.

So a vector quantity has a direction associated with it and that direction is very important 'cause if the direction is different, the result is different.

So if I've got an object here and it's stationary, it's at nought metres per second and I put an acceleration to the right on it, so the object accelerate to the right, it's gonna end up with a velocity towards right, perhaps four metres per second.

So we could describe that acceleration as positive acceleration and because acceleration is a vector, then if we accelerate something to the left, we get a different result, we get an object moving in the opposite direction to a velocity of minus four metres per second because we're describing directions as positive and negative.

So it is important to know which direction the object accelerates.

Let's check if you understand what I mean by acceleration and it being a vector.

Which statement best describes the acceleration of the car shown in the picture? So I've got a car, the car is speeding up as it moves downhill.

Is it A, the car is accelerating down the hill.

B, the car is accelerating up the hill.

C, the car is not accelerating or D, the car might not be accelerating, it might be accelerating up or downhill.

We just can't tell.

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

Hello again.

And the answer to that is the car is accelerating down the hill, it's getting faster downhill.

So we can say accelerating down the hill.

Well done if you've got that.

Another check of your understanding of acceleration here.

I've got a car, it speeds up from 20 metres per second to 30 metres per second as shown in that little diagram there.

Which two of these statements are correct? So pause video, read through the statements, make selection and restart.

Welcome back.

You should have chosen these two.

The change in velocity is 10 metres per second.

It's gone up from 20 metres per second to 30 metres per second.

So that's 10 metres per second increase and the car is accelerating to the right.

It's got faster in the right direction.

Well done if you've got those two.

We're now going to start looking at how to calculate accelerations.

And to do that we need a definition of what acceleration is.

Acceleration of an object is the rate of change in velocity and that means how much the velocity is changing every second.

And we have a mathematical expression for that and it's very similar to other expressions you may have seen before.

Acceleration is a change in velocity divided by the time.

And if we write that in symbols we use a for acceleration, delta-v for change in velocity in t for time.

So acceleration, a, is measured in metres per second squared.

We'll talk more about that in a minute.

Change in velocity delta-v is measured in metres per second and time is measured in seconds as usual.

I've just said that acceleration is measured in metres per second squared and that looks like a slightly unusual unit.

So let's quickly try and explain where that unit comes from.

So if we think about velocity, velocity is the rate of change of displacement or how much of displacement changes every second.

And mathematically we've said it's this.

Velocity is change in displacement divided by time and velocity is a distance divided by time according to that equation.

So to get the unit for velocity, what we do is we get the unit for distance of displacement and divided by the unit by time and that gives us metres divided by seconds or metres per second.

Acceleration as we said is the rate of change of velocity.

So we can do the same thing to try and find the unit for acceleration.

Acceleration is a change in velocity divided by time and as acceleration is a velocity or metres per second divided by seconds, we end up with metres per second divided by seconds, which is metres divided by second squared.

So the unit for acceleration is metres per second per second.

So now as we've seen the equation for acceleration, let's try an example calculation.

We're going to do this in symbols and in words.

So I've got a figure skater and the velocity increases for one metres per second to five metres per second in a time of two seconds.

Calculate the acceleration.

So if we do them words, we write out the full expression, acceleration is changing velocity divided by time and we substitute those values in.

The change in velocity is five metres per second minus one metres per second 'cause that's how much the velocity's changed and the time is two seconds and so we get acceleration of two metres per second squared.

If we did that in symbols, we'd write out the equation like this using the delta-v notation for change in velocity.

We put in the same values because obviously it's the same data and it gives us the acceleration just like that.

You can see that writing in symbols is much quicker.

So we're going to try a couple more examples.

I'll do one and then you can have a go.

And we're gonna use symbols because it's a bit quicker than writing out everything in full words.

So a bicycle speeds up from five metres per second to nine metres per second in two seconds.

Calculate the acceleration of the bicycle.

So first thing we do is we write out the expression, a equals delta-v over t.

a equals the change in velocity divide by the time.

And then we substitute in the two values and we're looking for the change in velocity.

So that is the final velocity minus the initial velocity.

And I put those two values in divided by the time and that gives us an answer of two metres per second squared.

Now it's your go so I've got a speedboat and it speeds up from three metres per second to seven metres per second in a time of five seconds.

Calculate the acceleration of the speedboat.

So pause the video, follow the same procedure as I did and calculate the acceleration please then restart.

Hello again and you should have written out the expression just as I did.

a equals delta-v over t then substituted in the values from the question, getting the change in velocity on the top, dividing that by the time and that gives an acceleration of 0.

8 metres per second squared.

Well done if you got that.

Now it's time for the second task of the lesson.

And what I'd like you to do is to calculate a range of accelerations for me please.

I've got four different questions there and I just want to know the size of the acceleration in each case.

You don't need to write out the direction for me.

So pause the video, work out the accelerations for those four and then restart please.

Welcome back.

Let's work through the solutions for each of those.

So achieve to accelerating from rest or stationary to 27 metres per second in three seconds.

And that's an acceleration of nine metres per second squared.

During takeoff for the rocket takes 10 seconds to each 200 metres per second.

And again you do the math and that gives us an acceleration of 20 metres per second squared.

Well done if you've got those two.

And the next couple, a car speeds up from 20 metres per second to 30 metres per second in five seconds and that gives an acceleration of two metres per second squared.

And finally the rollercoaster ride travelling from 0.

7 metres per second speeding up to 5.

6 metres per second in 0.

7 seconds.

And that gives an acceleration of seven metres per second squared.

Well done if you've got those.

And now we've reached the final part of the lesson and we're going to look at calculating deceleration, which is when an object is slowing down.

So far we've calculated acceleration for objects that are speeding up but objects can also slow down.

The velocity can decrease over time.

So for example, if I've got a cyclist travelling at six metres per second and they use their brakes, they can slow down to two metres per second so the speeds decreased and that will give a negative value for the acceleration.

And we call those negative values decelerations.

When an object is slowing down it's decelerating.

Let's see if you understood that with this quick check.

Car slows down from 30 metres per second to 20 metres per second.

Which two of these statements are correct? So pause the video, read through the statements, select two, and then restart please.

Welcome back.

Well you should have realised that the change in velocity is minus 10 metres per second, that indicates that the speed has decreased and that must mean that the car is decelerating.

Well only if we selected those two.

So we've already calculated accelerations using the equation, but we can use exactly the same equation to calculate decelerations.

The only difference is really that the acceleration calculated will end up giving us a negative value.

So let's try some deceleration calculations now using that equation.

I'll try one and then you try the next.

A bicycle breaks and slows down from eight metres per second to two metres per second in a time of four seconds.

Calculate the acceleration of the bicycle.

So as before I write down the equation, a equals delta-v divided by t and I substitute those two values in, being very careful to spot the initial and final velocities there.

And that will gimme two metres per second minus eight metres per second, divide by four seconds giving me an acceleration of minus 1.

5 metres per second squared.

So a deceleration there.

Now it's your turn.

I'd like you to calculate the acceleration here.

A sailboat slows from four metres per second to 0.

5 metres per second in seven seconds.

Calculate the acceleration.

So pause the video, try the calculation, and then restart, please.

Welcome back.

Your solution should look something like this and an acceleration of minus 0.

5 metres per second squared.

Well done if you've got that.

And now it's time for the final task of the lesson.

And I'd like you to calculate some accelerations based on the data here.

So we've got a car in a drag race accelerating in a straight line from rest to 66 metres per second in two seconds.

It passes the finish line at 90 metres per second and then opens a parachute and uses its brakes to slow it to 10 metres per second in 5.

0 seconds.

I'd like two calculations, please.

Calculate the acceleration of the car in the first two seconds of the race and then calculate the deceleration of the car as it passes the finish line.

So pause the video, and try and solve those two please, and then restart.

Okay, welcome back and let's have a look at the results of those calculations.

So I'll calculate the acceleration of the car and you should have had an expression, something like this and find an acceleration of 33 metres per second squared.

And that's a very high acceleration, a sort of acceleration you might feel on a rollercoaster as it goes around a bend and you can really feel acceleration acting on you.

Calculate the deceleration and I've got an acceleration value of minus 16 metres per second squared.

So I'm slowing down by 16 metres per second every second there.

Well done if you've got those two answers.

And now we're at the end of the lesson.

So here's a quick summary of everything we've learned.

Acceleration is the rate of change of velocity and it's a vector quantity, its direction is important.

Acceleration is calculated by this equation.

Acceleration is change in velocity, divided by time.

And in symbols that's a equals delta-v.

We use delta for change divided by time.

Acceleration is basically metres per second squared.

Change in velocity, delta-v is metres per second and the time is in seconds.

And an object that is slowing down is described as decelerating.

Well done for reaching the end of the lesson.

I'll see you in the next one.