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 measurement to find the acceleration or deceleration of an object.

And here's the 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.

The 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's 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, a starting and an end velocity.

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 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 changing 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 five meters per second, and what that means is the displacement is changing by five meters every second.

So after two seconds, the displacement would've changed by 10 meters.

Or we could have a velocity basically in kilometers an hour like this, two kilometers an hour means the displacement is changing by two kilometers every hour.

So let's practice 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 kilometers 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 the displacement divided by time or change in displacement there.

We'll write that down.

Velocity is 92 kilometers divided by four hours, identifying those two from the question.

And finally, do the calculation.

It's 23 kilometers 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 meters 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 divided by time.

Identify those two values in the question.

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

5 meters 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 traveling initially.

Well done if you 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 of 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 traveling east six meters per second and it speeds up to nine meters 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 round.

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

We substitute in the two values.

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

So just subtract those, and that gives a change in velocity of three meters per second.

And the velocity's changed in the eastward 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's 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 nine meters per second to nine meters per second, u, the initial velocity, is 0 meters per second and v, the final velocity, is nine meters per second.

If that sprinter then slowed down from nine meters per second to six meters per second, then u, the initial velocity, is nine meters per second and v, the final velocity, is six meters 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, traveling at two meters per second at the top and 4.

5 meters per second at the bottom.

Calculate the changing velocity of the skater.

So I'll write up my expression.

Changing 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 meters per second, and u being the initial velocity, 2.

0 meters per second.

Do that calculation.

It's 2.

5 meters 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 meters per second to 8.

5 meters per second while traveling 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 its 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 meters 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 five meters per second, then if we want to talk about movement to the left, we can just give a value that's negative, so -3 meters 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 five meters per second and it's caught moving down at -3 meters per second.

Calculate the change in velocity of the stone.

Well, as usual, I write out expression, changing velocity is v minus u, final velocity minus initial velocity.

And I very carefully put those two values in.

The final velocity was -3 meters per second and then I take away the initial velocity which was plus five meters per second.

So I get something like that.

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

Now, it's your turn.

A ball is thrown at a wall at six meters per second and bounces straight back at -5 meters 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's 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 six meters per second and a final velocity of minus five meters per second there.

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

So the change of velocity is -11 meters 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 meters per second.

It stalls and rolls down the hill at four meters 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 got a solution of -7 meters per second.

If we write down the mathematics for that, the change in velocity is -4 meters per second, minus three meters per second, giving a total change of -7 meters per second.

Well done if you 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 meters of the race.

I'd like you to complete that table to show the final velocity, the average velocity over those last 20 meters, 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 math 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 got them.

Now, it's time to move on to the second part of the lesson, and we're gonna 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 speeding up, say, from six meters per second to nine meters 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 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 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 its 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 0 meters 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 four meters 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 meters 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 meters per second to 30 meters 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 a selection, and restart.

Welcome back.

You should have chosen these two.

The change in velocity is 10 meters per second.

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

So that's 10 meters per second increase.

And the car is accelerating to the right.

It's got faster the right direction.

Well done if you 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 u divided by t.

So acceleration, a, is mentioned in meters 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 meters per second because they're velocities, and time, t, is measured in seconds as usual.

I've just said that acceleration is measured in meters 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 divide it by the unit by time, and that gives us meters divided by seconds or meters 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 meters per second divided by seconds, we end up with meters per second divided by seconds, which is meters divided by seconds squared.

So the unit for acceleration is meters 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 her velocity increases from one meters per second to five meters 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 there was five meters per second minus one meters per second.

We're 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 meters per second squared.

If we do that in symbols, we write out like this, a equals v minus u, so that's final velocity minus initial velocity divided by t.

Putting those two values in from the question gives us exactly the same expression, but we're just using the symbol a for acceleration and obviously that will give us the same answer, two meters 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 symbols in our calculations here.

So our bicycle speeds up from five meters per second to nine meters per second in two seconds.

Calculate acceleration of the bicycle.

So what I do is I write out the expression a equal v minus u over t.

a equals final minus initial velocity divided by time.

I substitute those two values carefully from the question, nine meters per second minus five meters per second, for v minus u, then divided by two seconds, and I then calculate the final answer.

It's two meters per second squared.

Now, it's your turn to calculate an acceleration, a speedboat speeds up from three meters per second to seven meters per second in five seconds.

Calculate the acceleration of the speedboat.

What I'd like you to do is follow 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, v, the final velocity, is seven meters per second, and the initial velocity, u, is three meters per second divided by the time, five seconds.

That gives an acceleration of 0.

8 meters 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, and let's have a look at the solutions for those.

So the cheetah's acceleration is nine meters per second squared, and you can see the math for that there.

The rocket, 20 meters per second squared.

Well done if you got those two.

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

And the rollercoaster ride, that's an acceleration of seven meters per second squared, Well done if you 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 traveling at six meters per second and they use their brakes, they can slow down to two meters per second, so the speed's 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 meters per second to 20 meters 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 realized that the change in velocity is -10 meters per second.

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

Well done if you 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 eight meters per second to two meters per second in four seconds.

Calculate the acceleration of the bicycle.

So what I need to do is to write up 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 two meters per second and my initial velocity is eight meters per second.

And when I do that calculation, means we've got a deceleration there.

So now you can have a go.

A sailboat slows from four meters per second to 0.

5 meters per second in seven seconds.

Calculate acceleration of the sailboat.

Pause the video, do the same calculation 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 -4.

5 meters per second squared.

Well done if you 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 meters per second in two seconds.

It passes the finish line at 90 meters per second and then opens a parachutes and uses its brakes to slow it to 10 meters 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 meters 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.

Calculating the deceleration, well, I get an acceleration of -16 meters per second squared there.

And so that's a deceleration of 16 meters 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 velocity divided by time.

And we can write that down in symbols as a equals v minus u over t.

Acceleration, a, is measured in meters per second squared, initial velocity, and we use the symbol u for that, and final velocity, with the symbol v, are both measured in meters 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.