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 help you during the lesson.

The first of them is velocity.

Velocity of an object is its speed in a particular direction.

Second is rate of change and the rate of change is how much a quantity changes each second or per second.

Then there's acceleration which we use to describe the speeding up or change of direction of an object.

And finally, deceleration which is when an object is slowing down.

And here are some definitions of those keywords that you can return to at any point in the lesson.

The lesson is 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 and an end velocity.

The second part of the lesson, we're gonna 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 gonna be looking at deceleration which is when objects are 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.

And 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 velocity of 5 metres per second, and what that means is the displacement is changing by 5 metres every second.

So after two seconds, the displacement would've changed by 10 metres or we could have a velocity basically 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 there.

Write that down.

Velocity is 92 kilometres divided by 4 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 is 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, 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 6 metres per second and it speeds up to 9 metres per second still east.

What's the change in velocity? Well, all we need to do is to find the change in velocity.

It's final velocity minus initial velocity, and it's very important to write it that way round.

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

We substitute in the two values.

So, the final velocity was 9 metres per second and the initial velocity was 6 metres per second.

So just subtract those and that gives a change in velocity of 3 metres per second.

And the velocity's changing the east with direction.

So, we should write that down as well.

Because we're dealing with change in velocity, we need to use two symbols.

One to represent the initial or starting velocity and another to represent the end velocity.

So the initial velocity is represented by the letter U and the final velocity is represented by the letter V.

We've got to be very careful when using those two symbols because they can look very similar when we write them down.

So I'll be very careful to say which one's which as I go along.

Some examples, so if I've got a sprinter and they're speeding up from not metres per second to 9 metres per second, U, the initial velocity is not metres per second.

And V, the final velocity, is 9 metres per second.

If that sprinter then slowed down from 9 metres per second to 6 metres per second, then U, the initial velocity, is 9 metres per second.

And V, the final velocity, is 6 metres per second.

Let's see if we can use those symbols properly.

I'll do one example and then you do another.

So I've got a skateboarder rolling down a hill in a straight line, travelling at 2 metres per second at the top and 4.

5 metres per second at the bottom.

Calculate the change in velocity of the skater.

So, I'll write up my expression.

Change in velocity is V minus U, making sure we get those two the right way around.

Substitute those values in.

V being the final velocity, it's 4.

5 metres per second.

And U being the initial velocity, 2.

9 metres per second.

Do that calculation.

It's 2.

5 metres per second.

Now, it's your turn.

I'd like you to calculate change in velocity here, being very careful to use the correct symbols.

A motorcycle speeds up from 3.

2 metres per second to 8.

5 metres per second while travelling in a straight line.

Calculate the change in velocity.

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

Welcome back.

Well, you should have written out is expression, change in velocity is V minus U, Final velocity minus initial velocity.

We substitute those two values in and that gives us a change in velocity of 5.

3 metres per second.

Well done if you've got that.

So, 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 5 metres per second, then if we want to talk about movement to the left, we can just give a value that's negative.

So -3 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.

Okay, let's see if we can do some calculations that involve negative velocities.

I'll do one and then you can do one.

A stone is thrown into the air at 5 metres per second and it's caught moving down at -3 metres per second.

Calculate the change in velocity of the stone.

Well as usual, I write out expression.

Change in velocity is V minus U, final velocity minus initial velocity.

And now very carefully put those two values in.

The final velocity was -3 metres per second.

Then I take away the initial velocity which was close to 5 metres per second.

So I get something like that.

Doing the maths, I get a change in velocity of -8 metres per second.

Now it's your turn.

A ball is thrown at a wall at 6 metres per second and bounces straight back at -5 metres per second.

Calculate the change in velocity of the ball.

So pause the video, follow the same procedures as I did, and then restart.

Hello again and so you should have written down the expression, change in velocity is final velocity minus initial velocity or V minus U.

Substitute those values in very carefully.

Looking at the question, we've got an initial velocity of 6 metres per second and a final velocity of -5 metres per second there.

Do the maths and that gives us -11 metres per second.

So the change of velocity is -70 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 3 metres per second.

It stalls and rolls down the hill at 4 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 up your answer, and then restart please.

Welcome back.

You should have got a solution of -7 metres per second.

If we write down the mathematics for that, the change in velocity is -4 metres per second minus 3 metres per second, giving a total change of -7 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 play 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 and the maths behind each of those calculations is shown here and you can then check how you should have got each of those results.

Well done if you've got them.

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 changing 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 is speeding up say from 6 metres per second to 9 metres per second, that 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's 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 shown 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.

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 is stationary.

So, its speed is 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 not metres per second and I put an acceleration to the right on it, so the object accelerates to the right.

It's gonna end up with a velocity towards right, perhaps 4 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.

So a velocity of -4 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 downhill.

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 the video, read through the statements, make your 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 the right direction.

Well done if you've got those two.

We're going to start calculating accelerations in a minute.

But before that, we need a definition of what acceleration is mathematically.

An acceleration of an object is defined as the rate of change of velocity, and that basically means how much the velocity is changing every second.

So mathematically, we express that like this.

The acceleration is the change in velocity divided by the time taken.

Or in symbols, A equals V minus divided by T.

So acceleration A is mentioned in metres per second and we'll talk a bit more about that unit in a little while.

Initial velocity and final velocity.

So U and V are both measured in metres per second because their velocities.

And time, T, 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 changing, displacement divided by time, and velocity is a distance divided by a time according to that equation.

So, to get the unit for velocity, what we do is we get the unit for distance or 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 in 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 second which is metres divided by second squared.

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

So as we've seen the expression for velocity now, we can try an example acceleration calculation.

What we're going to do is do that using words and symbols.

So I've got a figure skater and the velocity increases from one metres per second to 5 metres per second in a time of two seconds.

Calculate her acceleration.

So if we do that in words, we can start by writing out the expression.

Acceleration is change in velocity divided by time.

And then we substitute in the values.

The change in velocity was 5 metres per second minus 1 metre per second by trying to find the difference in velocity.

And the time is two seconds.

And when we do the calculation, that gives us an acceleration of two metres per second squared.

If we do that in symbols, we write out like this A equals V minus U.

SO that's the final velocity minus initial velocity divided by T.

Putting those two values in from the question gives us exactly the same expression what we're just using the symbol A for acceleration.

And obviously, that will give us the same answer, 2 metres per second squared.

Okay, let's try another couple of examples.

I'll do one and you do one.

And we're gonna be using the symbols in our calculations here.

So a bicycle speeds up from 5 metres per second to 0 metres per second in 2 seconds.

Calculate acceleration of the bicycle.

So what I do is I write out the expression, A equals V minus U over T.

A equals final velocity minus initial velocity divided by time.

I substitute those two values carefully from the question, 9 metres per second minus 5 metres per second for V minus U then divided by two seconds and I then calculate the final answer.

It's two metres per second squared.

Now at Jogo, to calculate an acceleration, a speedboat speeds up from 3 metres per second to 7 metres per second.

In five seconds, calculate the acceleration of the speedboat.

What I'd like you to do is to follow up the same procedure as I did to get the acceleration.

So pause the video and find the acceleration and restart please.

Welcome back and you should have written this out.

A equals V minus U divided by T.

And then we substitute those two values in.

The final velocity is 7 metres per second and the initial velocity, U, is 3 metres per second divided by the time, 5 seconds.

That gives an acceleration of 0.

8 metres per second squared.

Well done if you've got that.

Now it's time for the second task with 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 and let's have a look at the solutions to those.

So the cheetah's acceleration is 9 metres per second squared.

Although, you can see the math for that there.

The rocket 20 metres per second squared.

well done if you've got those two.

And the second too the car is speeding up, that's an acceleration of two metres per second squared.

And the rollercoaster ride, that's an acceleration of 7 metres per second squared, Although they got those two as well.

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 6 metres per second.

They use their brakes, they can slow down to 2 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 pleases.

welcome back.

Well, you should have realised that the change in velocity is -10 metres per second.

That indicates that the speed has decreased and that must mean that the car is decelerating.

Well done if we selected those two.

We've already calculated accelerations using this equation and we can use the same equation to calculate deceleration as well.

But we have to be aware that what we'll end up is with negative values.

Okay, it's time to try and calculate some decelerations now.

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

A bicycle breaks and slows down from 8 metres per second to 2 metres per second in four seconds.

Calculate the acceleration of the bicycle.

So what I need to do is the write out the acceleration equation as normal and then substitute in the values, but be very, very careful to identify initial and final velocity.

So my final velocity is 2 metres per second and my initial velocity is 8 metres per second.

And when I do that calculation, I get an acceleration of -1.

5 metres per second squared.

And that means we've got a deceleration there.

So now you can have a go.

A sailboat slows from 4 metres per second to 9.

5 metres per second in 7 seconds.

Calculate the acceleration of the sail boat.

Pause the video, do the same calculation as style as I did, and find an answer for acceleration and then restart.

Okay, so your stages should look something like this and you should get an acceleration of -9.

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.

You should have found the acceleration in the first two seconds of the race to be 33 metres per second squared, and that's quite a large acceleration.

You'd really feel that.

You might have experienced similar accelerations if you're on a rollercoaster or something like that.

Calculate the deceleration while I get an acceleration of -16 metres per second square there.

And so that's a deceleration of 16 metres per second every second.

Well done if you got those.

Okay, we've reached the end of the lesson now and here's a summary of everything we should have learned.

Acceleration is the rate of change of velocity and it's a vector quantity.

Its direction is very important.

Acceleration can be calculated with these equations.

Acceleration is change in velocity divided by time and we can write that out in symbols as A equals V minus U of T.

Acceleration, A, is measured in metres per second squared, initial velocity, and we use the symbol U for that, and final velocity, with the symbol V, are both measured in metres per second and the time T is measured in seconds.

An object that's slowing down can be described as decelerating.

So well done on reaching the end of the lesson.

I'll see you in the next one.