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Hi, my name is Mrs. Dennett.

And in this lesson we're going to be solving simple kinematics problems. So, what is kinematics? Well, it's a branch of mathematics concerned with the motion or movement of objects.

We're going to focus on three formulae.

These are sometimes called the SUVAT equations.

Let's have a look at these equations in more detail.

What do the variables represent? s represents the displacement.

This is distance but with a direction.

So for example, a ball falling one metre downwards.

u represents the initial velocity, that's the starting velocity, and v represents the final velocity.

You may be wondering why we're not using average speed here? We use velocity because velocity is speed in a given direction.

Speed only tells us how fast you travel in a certain amount of time.

So you might be travelling at 40 miles per hour.

Well, that's 40 miles per hour.

With velocity, you can say you're travelling 40 miles per hour in a northerly direction.

A negative velocity would mean you're travelling in the opposite direction.

So velocity is often positive or negative.

So here, minus 40 miles per hour would mean going in a southler direction.

a represents acceleration.

Acceleration is a rate of change of velocity over time.

So if the velocity is in metres per second, the acceleration is metres per second per second.

Which we write as metres per second squared.

And finally, we've got t, which represents time.

So let's have a look in more detail at how the formulae work.

So we're given this formula v equals u plus a t.

We want to use the formula to work out the velocity, that's the final velocity.

When u equals five, so the initial velocity is five, the acceleration is six, and time is 10.

So, we substitute our values into the formula and calculate to get the final velocity is 65.

Let's use the formula to work out u the initial velocity, when v is 75, a is six and t is 10.

Substitute the values into the formula.

And this time we're going to have to rearrange slightly because we're trying to find u.

So we get 75 equals u plus 60.

Subtract that from 75, and we get u equals 50.

Here are some questions for you to try.

Pause the video to complete the tasks and restart when you're finished.

Here are the answers.

These questions just involve substitution of the values given into the equation.

It's useful to start thinking about what each of the values means in context though.

Could you go through your answers and as an extra challenge, think about what units could be involved.

There will be more than one answer for some.

So for example, time can be measured in seconds, minutes, hours, et cetera.

Think about how this would affect the units of the other variables.

Let's have a look at the other formula, v squared equals u squared plus two a s We want to use the formula to work out the final velocity, when u is five, a is 3.

75, and s is 10.

So we put these values into our formula.

And be very careful here to think about the order of operations.

So we, calculate five squared first, and two, lots of 3.

75, times 10.

Which gives us 25 add 75, which is 100.

And then we need to remember to square root 100 to get the final velocity, which is 10.

Let's have a look at another example.

So this time, we substitute our values into the formula again.

What we're trying to work out the displacement s.

So we're going to have to do a little bit of rearranging.

So we calculate 10 squared is 100, two squared is four, and then we've got two times five times s, which is 10s.

Subtract four, from 100 to get 96, and then divide by 10 to get the displacement, which is 9.

6.

So now we're going to look at how these formulae work in a context.

We've got a cyclist starting from rest, so he's just getting on his bike.

And the cyclist accelerates at 20 metres per second squared for six seconds.

And we want to work out the final velocity of the cyclist.

So let's write down the information that we've got.

We've got, the cyclist starts from rest.

So this tells us that the initial velocity must be zero because there's no movement there, okay.

So u is equal to zero.

And we can see that they accelerate at 20 metres per second squared.

So, the acceleration, a is 20.

And then finally, we've got the time which is six seconds.

And we want to work out the final velocity that's v.

Now we have to decide which of these formulae is most appropriate for this question.

Well, we've got u, a and t.

We've got values for u, a and t.

And we want to work out the final velocity v.

So there's no mention of s, the displacement here, so we want to be using the first formula.

So we substitute these values into our first formula, like so, and work out that the final velocity is 120 metres per second.

Here are some questions for you to try.

Pause the video to complete the task and restart when you are finished.

Here are the answers.

Questions two and three just involve substitution, but make sure that you follow the rules of the order of operations.

So indices first, then multiplication and then addition.

For question four, we use the formula, v equals u plus a t.

As we know that u equals zero, so the object starts at rest, so the initial velocity is zero.

The acceleration a is equal to eight metres per second squared, and the time t is 5.

5 seconds.

Substitute these into the formula to get the final velocity of 44 metres per second.

That's all for this lesson.

Remember to take the exit quiz before you leave.

Thank you for watching.