Video Transcript
The displacement, ๐ , of an object travelling with uniform acceleration, ๐, can be calculated using the formula ๐ equals ๐ข๐ก plus a half ๐๐ก squared, where ๐ข is the initial velocity and ๐ก is the time. Thereโre two parts to this question. The first part, Make ๐ the subject. And the second part, calculate the acceleration of an object that has started from rest and travelled 200 meters in eight seconds.
So if we have our formula, which is ๐ equals ๐ข๐ก plus half ๐๐ก squared. And if we want to make ๐ the subject, well, the subject means we want the ๐ on its own. So the first thing weโre gonna do is subtract ๐ข๐ก from both sides of the equation. Thatโs cause that will leave us with a half ๐๐ก squared on the right-hand side. So now, when we subtracted ๐ข๐ก from both sides of the equation, we get ๐ minus ๐ข๐ก is equal to a half ๐๐ก squared. And now, because weโve got a half ๐๐ก squared on the right-hand side, what weโre gonna do is multiply both sides of the equation by two. And thatโs because that will remove the half that weโve got removed the fraction.
So when we do that, we get two multiplied by ๐ minus ๐ข๐ก is equal to ๐๐ก squared. Thatโs because if we have a half multiplied by two, you get one. So then, all we need to do is divide by ๐ก squared because that will leave ๐ on its own. And once we do that, weโll have two multiplied by ๐ minus ๐ข๐ก over ๐ก squared is equal to ๐. So therefore, having made ๐ the subject, weโve got ๐ is equal to two multiplied by ๐ minus ๐ข๐ก over ๐ก squared.
Great. Now, letโs move on to the second part. And in the second part, we need to calculate the acceleration of an object that has started from rest and travelled 200 meters in eight seconds. So now to solve any question like this, what Iโd do first is write down the information Iโve got. So we know that ๐ข is equal to zero because this is the initial velocity. And we know that because weโre told that the object starts from rest. And for an object to start from rest, that means that itโs not gonna have any velocity at the beginning. So ๐ข is equal to zero.
Then, the next thing we know is that the distance, which is ๐ , is equal to 200 meters. And thatโs because weโre told the distance travelled is 200 meters. Then, we also know the time because this is eight seconds and the acceleration ๐ is what weโre looking for. So we havenโt got that yet. Okay, now weโve got our values, we can just substitute them into our equation. And the equation weโre gonna use is ๐ equals two multiplied by ๐ minus ๐ข๐ก over ๐ก squared because what weโre trying to find is ๐, which is the acceleration.
So now, to work out the acceleration, weโre gonna have ๐ is equal to two multiplied by. Then, weโve got 200 cause thatโs our ๐ , cause thatโs our distance minus ๐ข, which is zero multiplied by our time, which is eight. And then this is all divided by our time squared, which is eight squared. So this gives us that ๐ is equal to 400 divided by 64. And thatโs because we had two multiplied by. And then, youโve got 200 minus zero multiplied by eight. Well, 200 minus zero cause zero multiplied by anything is just zero gives us 200. Two lots of 200 is 400 and then divided by eight squared and eight squared is 64.
Then, if we simplified it by dividing both the numerator and denominator by four, weโre gonna get 100 over 16. And then once more divided by four, weโre gonna get 25 over four cause 100 divided by four is 25. 16 divided by four is four. So then, we can see that four goes into 25 six times with one remainder. So we get six and a quarter. And when we turn it into a decimal, itโs 6.25. Then, we know that the units are gonna be meters per second squared because thatโs the measurement weโre gonna use for acceleration.
So we can say that if we make ๐ the subject, we get ๐ equals two multiplied by ๐ minus ๐ข๐ก over ๐ก squared. And if we calculated the acceleration of an object that has started from rest and travelled 200 meters in eight seconds, then the result is 6.25 meters per second.
