Lesson video

Hello there, my name's Mr. Forbes, and welcome to this lesson from the measuring and calculating motion unit.

In the lesson, we're going to be looking at changes in velocity and using those to calculate acceleration.

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 sub 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 there's acceleration, and acceleration means when 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.

This lesson's in three parts, and in the first part we're going to be looking at changes in velocity.

We're gonna be looking at starting or initial velocities and end or final velocities, and using those two to find out how much our velocity's changed.

Then we're gonna use that change in velocity in the second part of the lesson to calculate acceleration, where we'll need to know how long it took for that velocity to change.

And in the final part of the lesson, we're gonna be looking at deceleration, which is when an object is slowing down.

So when you're ready, let's start 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 metres per second, and what that means is the displacement is changing by 5 metres every second.

So after 2 seconds the displacement would've changed by 10 metres.

Or we could have a velocity measured in kilometres an hour, like this, 2 kilometres an hour means the displacement is changing by 2 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 4 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.

We write all of 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 that average velocity.

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

Welcome back, and you should have done your calculation like this.

So first of all, write out the equation, velocities 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, 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 at 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 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 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 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 would 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 changes its velocity by 4 metres per second, then delta-v is 4 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 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 what they 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 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 the video, work out your solution and then restart.

Welcome back, while using the symbol correctly, delta-v's 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 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.

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

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

So I've got a negative velocity there.

Calculate the change in velocity for the stone.

And what I do is, I write down the expression delta-v's final velocity minus initial velocity, and there carefully identify both of those from the question.

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

So I've got a sum there of -3 metres per second, minus 5 metres per second, that gives me a change in velocity of -8 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 6 metres per second and bounces straight back at -5 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 put in those two values.

We've got a final velocity of -5 metres per second, and an initial velocity of 6 metres per second.

So when we subtract those, we get an answer of 11 metres per second.

Well done if you 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 found a solution of -7 metres per second.

If we put that in the mathematics, delta-v's final velocity minus initial velocity, substitute those two values, being very careful to take into account direction, it gives a change in velocity 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 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 gonna use those changes in velocity that we've seen 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 6 metres per second to 9 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'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 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 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 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.

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 in the right direction.

Well done if you've got those two.

And here's a more challenging question about acceleration.

Sam throws a ball up, it reaches a maximum height to X, if you look in the diagram you can see the ball, and the position's shown at equal intervals to time, every 1/10 of a second, say.

So it reaches a maximum height to X, describe the acceleration of the ball as it rises, and only as it rises, please.

So pause the video, read through those options, select the correct one, and then restart, please.

Welcome back, you should have chosen the ball is accelerating in a downwards direction.

What's happening though is it's vertical speed is decreasing so it's slowing down, so it must be accelerating downwards.

And if we continued to see what happens to that ball after it's reached high X, you'd see it starts moving downwards, getting faster and faster and faster.

So well done if you selected C.

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 of 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 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 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 the 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 of displacement and divide it 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 on metres per second divided by seconds, we end up with metres per second divided by second, which is metres divided by seconds 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 their velocity increases from 1 metres per second to 5 metres per second in a time of 2 seconds, calculate the acceleration.

So if we do that 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 metres per second minus 1 metres per second, 'cause that's how much the velocity has changed, and the time is 2 seconds, and so we get acceleration of 2 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 5 metres per second to 9 metres per second in 2 seconds, calculate the acceleration of the bicycle.

So the first thing we do is we write out the expression, A equals delta-v over T, 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've put those two values in, divided by the time, and that gives us a an answer of 2 metres per second squared.

Now it's your go, so I've got a speedboat and it speeds up from 3 metres per second to 7 metres 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.

Now 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 9.

8 metres per second squared.

Well done if you've got that.

So far we've just used fairly simple values for velocities, but accelerations can be extremely large because there can be very quick changes in velocity.

And to calculate those accelerations, we have to resort to using standard form.

So we'll look at an example of that.

I've we've got a question here.

During a sporting event, a bullet's fired from a rifle at a target, the bullet takes 3.

0 milliseconds to reach a velocity of 0.

6 kilometres per second, calculate the acceleration.

So to solve that we use the same equation, but we can use standard form for the values.

So we write out the initial equation, A equals delta-v divided by T, and then we substitute in the values, being very careful so at the start there, on the top line, we're calculating the change in velocity.

And the velocity was 0.

6 kilometres per second, define velocity, so I'm gonna write that in standard form as 0.

6 times 10 to the 3 metres per second, and the initial velocity was 0 metres per second.

Then we're gonna divide by the time, and the time is 3 milliseconds.

So I can write that as 3.

0 times 10 to the minus 3 seconds.

Then when I do that calculation, I get a very large acceleration of 2.

0 times 10 to the 5 metres per second squared.

So standard form makes that mathematics easier to do.

So a more challenging question for you here, I'd like you to calculate acceleration using some standard form.

A particle accelerator can increase the velocity of an electron from 0 metres per second to 1.

0 times 10 to the 8 metres per second in a time of only 0.

02 seconds.

Calculate the acceleration of the electron, and give you answer in standard form.

So we'll pause the video, work out the solution to that and then restart, please.

Welcome back, and the solution's shown here, A equal delta-v divided by T.

We substitute the values in using standard form, and then put that through the calculator and it gives us A equals 5.

0 times 10 to the 9 metres per second squared.

A huge acceleration.

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, let's work through the solutions for each of those.

So a cheetah accelerating from rest, or stationary, to 27 metres per second in 3 seconds, and that's an acceleration of 9 metres per second squared.

During takeoff for the rocket, takes 10 seconds to reach 200 metres per second, and again, we 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 5 seconds, and that gives an acceleration of 2 metres per second squared.

And finally, the rollercoaster ride travelling from 9.

7 metres per second speeding up to 5.

6 metres per second, in 0.

7 seconds.

And that gives an acceleration of 7 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 gonna start looking at deceleration and calculating that, and it's 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 and they use their brakes, they can slow down to 2 metres per second, so their 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.

A 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 -10 metres 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 brakes and slows down from 8 metres per second to 2 metres per second in a time of 4 seconds, calculate the acceleration of the bicycle.

So as before, I write down the equation, 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 give me 2 metres per second minus 8 metres per second, divide by 4 seconds, giving me an acceleration of -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 4 metres per second to 0.

5 metres 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 -0.

5 metres per second squared.

Well done if you've got that.

Now we're going to look at more complicated scenarios that involve objects speeding up and slowing down.

So when you've got an object that's moving in one direction and then starts to reverse, the object must have slowed down to reach 0 and then sped up in the opposite direction.

So for example, I've got a car and it's moving forward, so I've got a positive velocity written down here of 5 metres per second.

Then the car would decelerate, or accelerate backwards, until it stops and reaches 0 metres per second.

And if that acceleration continues, what's gonna happen to the car? Well, it's going to start moving backwards in an opposite direction, so it's gonna end up with a negative velocity.

Throughout that motion of slowing down and speeding up in the opposite direction, the acceleration was always in the same direction.

So that acceleration causes the object to slow down and then speed up in the opposite direction.

You have to take a great deal of care when you're dealing with objects that change direction when you're calculating acceleration.

So let's look at an example.

I've got a ball and it's rolled up a slope with a velocity of 3 metres per second, but then it rolls back down again, so it slows down and then it starts rolling back down that slope.

After 4 seconds, it's travelling down the slope with a speed of 2 metres per second, calculate the acceleration of the ball.

So to do that, I've gotta be very, very careful and write out the initial velocity and final velocity.

So the initial velocity going up the slope 3.

0 metres per second, and the final velocity is going down the slope, so we've got a negative velocity of 2.

0 metres per second.

We calculate acceleration as we do before, write out the equation, substitute those two values in very carefully.

So if you look, I've got -2.

0 metres per second there for the final velocity, put in your values and I'll get an acceleration of -1.

5 metres per second squared.

Let's check if you can do a calculation that involves change of directions.

So I've got a stone, it's thrown vertically upwards, into the air, at a speed of 8 metres per second.

It falls back down to the ground after 1.

6 seconds and it's travelling downwards at a speed of 8 metres per second.

Calculate the acceleration of the stone.

So pause the video and see if you can work out the acceleration, please.

Welcome back, and here's the stages you should have used.

Write out the equation, very carefully take the values from the question.

So I've got a final velocity of -8.

0 metre per second, and an initial velocity of 8 metres per second, and divide that by the time, and that gives me an acceleration of -10 metres per second squared.

Well done if you've got that.

Okay, we're at the final part of the lesson now, and I've got a couple of calculations about acceleration for you to do.

So what I'd like you to do is pause the video, read through the questions, do the two calculations and restart, please.

Okay, welcome back, and let's have a look at the solutions to those two questions.

Calculate the acceleration of the ball when it was launched.

Well, we write out the expression for acceleration, carefully substitute in the two values and we get acceleration of 12.

5 metres per second squared.

And calculate the acceleration of the ball when it hits the flipper, well again, reading the question very carefully, we've got to look at the initial and final velocities and take into account the directions, and that gives an acceleration of -56 metres per second squared.

Well done if you've got those two.

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 based in 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.