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 then 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.

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

And there's acceleration, and acceleration means on an object speeding up or changing direction.

And deceleration, which we use for slowing down or changing direction.

And this is a set of definitions of those keywords that you can return to at any point during 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, starting and then end velocity.

In 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 going to be looking at deceleration, which is when objects 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 5 meters per second, and what that means is the displacement is changing by 5 meters every second.

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

Or we can have a velocity based in kilometers an hour like this, 2 kilometers an hour means the displacement is changing by 2 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 4 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 displacement divided by time, or change in displacement there.

We write that down, velocity is 92 kilometers divided by 4 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, the 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'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 traveling east 6 meters per second, and it speeds up to 9 meters per second still east.

What's the change in velocity?

Well, all we need to do is to find the change of velocity, its 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 9 meters per second, and the initial velocity was 6 meters per second.

So just subtract those, and that gives a change in velocity of 3 meters 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 can 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 4 meters per second, then delta v is 4 meters 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 traveling at 2 meters per second at the top and 4.

5 meters per second at the bottom, calculate the change in velocity of the skater.

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

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

5 meters per second, and the initial velocity 2.

9 meters per second.

And I get my answer, it's 2.

5 meters 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 meters per second to 8.

5 meters per second.

Pause the video, work out your solution, and then restart.

Welcome back.

While using the symbol correctly, delta v is final velocity minus initial velocity.

We substitute the two values carefully from the question, and that gives us a delta v, 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 5 meters per second, then if we wanna talk about movement to the left, we can just give a value that's negative.

So minus 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.

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

A stone is thrown into the air at 5 meters per second.

It's caught when it's moving downwards at minus 3 meters 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 I carefully identify both of those from the question.

The final velocity was minus 3 meters per second, and the initial velocity was 5 meters per second, so that was a positive value.

So I've got a sum there of minus 3 meters per second minus 5 meters per second.

That gives me a change in velocity of minus 8 meters per second.

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

So a ball is thrown at a wall at 6 meters per second, and bounces straight back at minus 5 meters 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 put in those two values.

We've got a final velocity of minus 5 meters per second and an initial velocity of 6 meters per second.

So when we subtract those, we get an answer of 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 driving up a hill at 3 meters per second.

It stalls and rolls down the hill at 4 meters per second.

What's the change in velocity of that car if we take it up as being the positive direction?

So pause the video, work up your answer, and then restart, please.

Welcome back.

You should have found a solution of minus 7 meters 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 7 meters 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 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 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's speeding up, say, from 6 meters per second to 9 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 accelerate to the right, it's gonna end up with a velocity towards right, perhaps 4 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 to a velocity of minus 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 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 down the hill?

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 your 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 in the right direction.

Well done if you've got those two.

We're now gonna 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'll 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, and t for time.

So acceleration, a, is measured in meters per second squared, we'll talk more about that in a minute.

Change in velocity, delta v, is measured in meters per second.

And time 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 or 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 of velocity or meters per second divided by seconds, we end up with meters per second divided by seconds, which is meters divided by second squared.

So the unit for acceleration is meters 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 their velocity increases for 1 meters per second to 5 meters per second in a time of 2 seconds.

Calculate the acceleration.

So if we do them in words, we write out the full expression, acceleration is change in velocity divided by time, and we substitute those values in, the change in velocity is 5 meters per second minus 1 meters per second, 'cause that's how much the velocity's changed, and the time is 2 seconds, and so we get acceleration of 2 meters per second squared.

If we did that in symbols, we'd write out the equation like this using the delta v notation for changing 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 5 meters per second to 9 meters per second in 2 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 divided 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 have put those two values in, divided by the time.

And that gives us an answer of 2 meters per second squared.

Now, it's your go.

So I've got a speedboat, and it speeds up from 3 meters per second to 7 meters per second in a time of 5 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 meters per second squared.

Well done if you've 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 a cheetah accelerating from rest or stationary to 27 meters per second in 3 seconds.

And that's an acceleration of 9 meters per second squared.

During takeoff for the rocket, it takes 10 seconds to reach 200 meters per second.

And again, we do the math, and that gives us an acceleration of 20 meters per second squared.

Well done if you've got those two.

And the next couple, a car speeds up from 20 meters per second to 30 meters per second in 5 seconds, and that gives an acceleration of 2 meters per second squared.

And finally, the rollercoaster ride, traveling from 0.

7 meters per second, speeding up to 5.

6 meters per second in 0.

7 seconds.

And that gives an acceleration of 7 meters 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, and I've got a cyclist traveling at 6 meters per second, and they use their brakes, they can slow down to 2 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 minus 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.

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 8 meters per second to 2 meters per second in a time of 4 seconds.

Calculate the acceleration of the bicycle.

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

So a deceleration there.

Now, it's your turn.

I'd like you to calculate the acceleration here.

A sailboat slows from 4 meters per second to 0.

5 meters per second in 7 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 meters 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 meters per second in 2 seconds.

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

0 seconds.

And I'd like two calculations, please.

Calculate the acceleration of the car in the first 2 seconds of the race, and then calculate a 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 meters per second squared.

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

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

So I'm slowing down by 16 meters per second every second, though.

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 a equals delta v, we use delta for change, divided by time.

Acceleration is basically meters per second squared.

Change in velocity, delta v, is meters per second, and a 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.