A Level Mastery - A DECEPTIVELY Tricky SUVAT Question

okay so if we have a look at this question here we have another nine Mark super about question again something very typical to come up we have a l accelerates uniformly from 5 to 20 m/s in 30 seconds find how far it travels whilst accelerating so realistically again we probably don't need a diagram for this one but I always draw diagrams just as a good habit so let's quickly discuss all the different ways that I'm going to help you in your GCC or a level maths careers first of all I wanted to talk to you about the YouTube members this is a really costeffective way of getting tutoring so I'm going to do weekly live streams for GCSE and a-level maths and that all comes for £18 a month and you get at minimum an hour of tutoring per week in these live streams at the moment they're quite small so you basically get tuition for about £450 an hour which is really really cheap the second thing is the patreon for those of you doing a level maths I have already completed as stats on my patreon is a full class with worksheets mark schemes videos I answer all the questions we're going to do exam papers and everything that needs doing we're halfway through mechanics as of yet and lastly there's tuition I still have places in my group classes for a level maths and GCSE Maths for GCS it's £30 an hour and for a level is40 per hour so if you want to let me know if you're interested just email me or join the Discord where I'm very very active all the time anyways back to the video I'm going to represent the Lor as just a little box and it goes from 5 m/s and it goes to 20 m/s and we want the actual distance that it travels in that time and that time is 30 seconds so again we can write out our suat equation so we have S is equal to don't know that's what we want U is equal to 5 b is equal to 20 a is equal to don't know and T is equal to 30 now the cool thing about suat is that as long as you have three variables you can work out the other two guaranteed so we can get straight to s s from here now of course because we have three variables we could also work out a and then work out s if we want to so it really is up to use if you get stuck on how to get from these three variables straight to S think about well how do I work at a instead then and then use a different equation that's the beauty of it as long as you have three variables you're golden now of course the equation that has s u v and T in it is actually s equals U + v/ 2 T so if we sub that n we have 5 + 20/ 2 * 30 and we can get that out now so let's pull out our calculator so that's going to be 25 over 2 which is 12.5 * 30 probably didn't need a calculator for that but whatever 375 m is how far it travels now of course that's not too bad so what you'll find with a lot of suat questions is the first part is quite quick so we're going to get three marks just for that really really really fast but the real meat of the question is the six or seven marker that you have afterwards or you have multiple other parts as well but find in seconds corrector 2dp the length of time it takes for the lobby to cover the first half of this distance and you know what I find that this happens quite a lot where students get a bit stuck on this now first of all let's just write out what we know well s is going to be half of 375 so if I just quickly divide that by two on the calculator we get 187.5 m 1 8 7.5 M and actually I didn't need put the M but whatever U is still five cuz it's the first half of the distance if it was the last half of the distance we would know V is 20 right uh V we don't know a we also don't know and T is going to be what it says first half of the um well we want the times we don't have that so as you can see we're kind of screwed because we have only two known variables now there are a few different things you can do in order to work out exactly what's going on and here's what I would do if you remember when we do suat we have constant acceleration so I could work out acceleration from part A and it would be the same as the acceleration in Part B because remember the acceleration has to be constant throughout the whole thing so from a if we use the um part A equations we can say that a is equal to B- U / T so 20 - 5 over 30 which is going to be 15 over 30 which is a half so 0.5 that's my new value for a and now we have everything we need s equal UT plus half a^2 and that is where a lot of students lost marks because they didn't and this is a really cool thing with a level mats if you really want to get that a star if you really do want to get there and also impress people in your interviews for universities you need to understand the maths it's not good enough to be able to regurgitate information like you can in GCSE you have to understand why you're doing it and again that's how you get to the A's and a Stars okay you need to understand this question is not difficult if you understand that sua is constant acceleration which means the acceleration from part A will give you part B now there are a few lucky people who happened to work out a in part A and then then work out s but most people jumped straight to S and they didn't know a jumped to the second part and got stuck I only know two variables it's impossible it's not impossible it can't be impossible so enough of me kind of smack talking you uh that would be 5T plus a half a t^2 well a half a is going to be 0.25 T ^2 uh shove everything over to the right hand side will probably be the easiest and write it out as a quadratic equation so like like so and now all we need to do is use our calculator that's six Mar Mar that's why I love mechanics you get a lot of marks for realistically not that much work but you have to use your brain and that's the bit that a lot of people get struggle on two polom degrees two so 0.25 in front of the squared ter there's a five in front of the linear term and there is a - 187.5 for the constant term at the end and we get two values of course we do um I probably haven't given myself enough space though 34 and then we're also going to get -10 - 5 < tk34 now which one are we going to go for we are going to go for the positive value because keep in mind time cannot be negative the reason why we get Negative answers here is because it's a quadratic model okay so because we're assuming that our values are going to follow a u shape or an N Shape there's going to be two values for every single um point on there even if it doesn't make any sense because we tend to be looking at only the first half or the last half of the curve so we're going to take positive value which is it has to be this one so that is a bit lazy of me though so let's go back to the normal mode Let's actually work out what it is does it say to any so it says to two decimal places so let's quickly um sub that in and see what we get so -10 plus < TK 34 5un 34 even that is correct and it should be -1 come on here we are shocking thank you calculator 19 it says just two decimal places so T is equal to 19.15 seconds to two decimal places again I'd always recommend writing the exact value as well just so the examiner can see but that here is six marks not that bad in my opinion