Of t if I'm distance between two points and pasis instantly at rest. Okay. V is six what t is zero? Minus eight D T you个。Two squared I. This is accelerate. Six. Yes so six C T is zero, so c equals six so velocity equals two t squared -80 plus six. Okay, two points post Portugal is instantly instantaneously arrest. So. Previous is zero. Two squared -80 plus six equals zero t squared. Two t minus t minus. Dividivide it by two, so t squared -14 plus three. Wouldn't fall Yeah wouldn't fall. What a three. Three square red minus four t plus three Yeah so t equals one or two equals three. Second, and then. Okay, I say it's going to be two scminus 80 plus six. Dt so two cubed over three. -14 squared plus 60 plus c. And this when t is one. So it's gonna to be. I it over three when t is three. But can't be zero good. Velocity of a partigal after t seconds ago given by v equals 60-2m per second. After 5s, the displacement is 75m from o. Find an expression for the displacement. Find displacement half to 10s. 60 minus two. 60 squared. Equal 20. Plus c it the. 70 525735 square miles ten. 2575 so c equals ten. So then it's gonna be. 秋? Find the displacement after 10s. Equals three 100 minus two times ten plus ten equals 300-20 plus ten 200 and. Oh Yeah, 290. Okay, so I'm done. Okay, let's let's see what you got. Okay, so for one av equals two t squared -80 plus six Yeah and then for b eight over three. Yeah, perfect. Good. Okay, very good start. But the next ones, Yeah Oh sorry, Yeah, Yeah, Yeah, Yeah, Yeah, Yeah, Yeah, Yeah, Yeah. So the question 22a is three t squared minus two t plus ten. Two b is 290m. Yeah, okay, okay. A three particle p moves in a strminso that at the time t seconds, it's acceleration 8m per second squared. Get one by. What is this? Equals zero, p is at rest. Find this speed of t when the t equals three, t equals six. Okay. So when t equals three. So it's zero smaller equal to t smaller equal to three. So we use 14 minus t squared. C square red. Two t squared. Minus a third t cubed plus c. T equals zero, v equals zero. Yes c equals zero. B equals two square -30 cubed. Equals three. A second. T equals six, so you're going to use 27 over t squared. Plus one. Eato cube she no. So I don't get like how do you integrate 27 over t squared? Like how do you make it work? Rewrite it as 27 times t to the power of minus two. Okay. Yeah all right. Thank you, sir. T. That's tea. Minus t minus t 57 over minus t. The also. A equals six. You don't get anything. You see this. 27. Hello. I'll find like 11. Straight 90s for team. Okay. So 70 mint squared integrates 70d minus t squared dt equals. Two cubed three. Yeah. E mint squared. So for full aid, do I use differentiation instead of integration? Yeah okay, Yeah. Set v equals seven minus two t that's a. A. Find the total distance traveled by p in the first 10s. It's 5s and another 5s. So for four b, because I there's like 10s, so there's like the first formula and the second one. So like do I like split them into like two, 5s or do I like need to like do something? No. Yeah. For b, you're right. You have to split it up into two sections and you have to treat it as the first function for the first 5s and then the second function for the next 5s. Yet, okay, 5s, 5s. 17. Thank you. I love this. Our second to over two mintwenty 53. What's this? Five, six? And then. 5s 20 55 over six plus 25. 430 56. Okay, side that. You got some answers. Three A I got first three a. 9m per second. And then for three B, I only got up to like the light integration part. I'm not sure how to do the rest because I the three bildings with it. Yeah. Yep. So you need to integrate when. So when t is six, you want to find the speed, so you need to use the second function. Yeah. So you have a is 27 over t squared or a is 27t to minus two. Integrate thatgive you -27t to the minus one plus c and then you can find the plus c term because they tell you that at t is zero, p is at rest. So therefore, when two is zero, v is zero. Hang on, hang on, no, no, no, no, no, no, no, no, no, no, no, no, no, no, you will, sorry, you will use the boundary of when t is three. Okay. Let's still use t equthree Yeah because you need to sort of assume that the there's a continuous there's a continuous section between the 14 minus t squared to the 27 over t squared. So when t equals three, it has to the speed has to match both of them. Okay. So when you suthem when t is three, you're going to get twelve minus twelve minus nine Yeah which is sorry. No, you'll have no, you'll have to use them. You have to use this. The one that you just worked out that you got v is -27t to the minus one plus c. You're just going to have to use that and use the fact that it's continuous over that boundary. And work out the constant of integration from there. Okay. C is it's going to be minus nine. V equals 9m per second, so nine equals minus nine plus C C equals 18 and then c equals 18. V is going to be 27 over minus t plus 18 plus 18. V loeighteen minus 3:17. So v equals 18-27 over six是80 minus。4.5 13 five. We don't v so we get and we get v okay, I got v equals 13.5m per second. Yeah Yeah okay, that's Yeah and question four for a acceleration equals minus one. And four b 425 over 6m. Yeah, lovely. Perfect. Great. That's great. Okay, the velcity of a particle after t second is given by b was 60 minus two t squared. To sit in, find the time at which the acceration of the particle is zero. See you. The the differentiation. Six -14t. Zero six -14 equals zero. O轮。It's pasp moonly axaxis x axis expleration of p at times t second is 60-24. This was measured in the position of x direction initially the over with the velocity of of 60m second that the particle never travelthe native x. It's e -24. E T. C square red f 2:24t equals 3080 squared -24 plus c initially, the path goes at o with a velocity of 60. So v zero equals 62 plus 60. Three t squared minus eight plus 20 never, never travel, never travel in the negative x direction. So for six a, do we use like the discriminant? The six a Yeah. I would get the velocity as a function of time and then just show that just show that it's a positive quadratic. You could use the disscriminant, but you could also just put it in a in a completed square put amount. Yeah, all right. Minus. Find. It's t minfour squared by the 16 60 minus four square -60 plus 20t minus four squared plus four. Green e minus four square ared plus four. This is always positive positive, positive, always large positive. Yep. My distance traveled by the particle in the first 10s. 20 square -20 40 plus 60 of course this is b cubed over three t cubed -20 14 squared over to twelve squared plus 60t plus c. First 10s. So initial. So c is zero. So 100. No, that's cute. 1000-12012 hundred plus 600. So it's. 400m, okay? Okay for question five t equals 1.5s. And then question six, so completed the square. So it's three times brackets. Brackets t minus four squared, brackets ts plus four. So because t minus four squared is going always going to be positive and there's plus four and times three, so it's always going to be positive. And then six b is 400m. Did you get 400? Yeah, Yeah, Yeah, 400 is good. Okay, let's do these ones. It's called p moves in the single straight line, such as t seconds, t is logreater or equal to zero. This velv means ves percent is given back goes twelve minus two t squared. Distance, velocity. 能们老是一。I support it. Great. I don't know, it's integration. 40 but it's duty cubed 23t cubed. First, second. So it's twelve minus two over three. It's. 30 over three minutes the second. The value of t will p change this direction of the motion. Nothing nice. So what does it mean by like changing direction of the motion that means that v, the velocity goes from positive to negative or negative to positive, so it will temporarily be zero. Okay, the v equals zero. Okay, so twelve velocity direction velocity. The torana twelve minus two t squared is going to be equal to zero T T squared. T squared equals six t root six. Okay, fatigue als through 6s. I at the that he returns to sapoints. Starting point. So it must be distance equals zero. So there's twelve minus two thircubed equals to zero. Take t out times t squazero. T zero twelve 1:30t square equal als zero. 现在起欢。在18呢个时。It today goes three route to. Yeah it's three rotwo seconds. Okay. Question travels the time so that at time t seconds after possible o, its displacement from O X meters equals T Q to -15t squplus 62t. Velocity displacement to velocity. So it's differentiation. Equals what's is this three t squared -30t plus 60t. Initial velocity. To zero v. Equals 62m per second value of t, which p has zero acceleration. Acceleration velocity to acceleration. So it's differentiation 1630. A equals zero, 60, but 30 equals zero equals 5s. Okay okay okay. All right, so I'm done. Okay. Let's hear what you got. Okay, so 47A I got 34 over 3m. Yeah 43 good. Seven route six square rosix c three rotwo seconds. Yeah, three root two and then for eight av equals 62m per second. Question b, time equals 5s. Yeah, perfect. Let's see if we can squeeze a few more in. Oh, he travels along the straight line. Over for that time. But if urjust raised. Displement. I lost this place ement with lost seasuits. Yeah. Plus 4860 squred minus the. 1836 plus 48, so v equals zero and we divide them by six. Yes, we had t squared minus six t plus 18 equals zero, so 42t two minfour 30 equals two equals four and and. So, so distant traveled in the first 5s. V equals six t minus two t minfour. She. Yeah. So I don't get how do you do nine b. So supposed distance traveled in first. In the first 5s. So you would work out when the displacement goes to zero again. Because you want to ignore when it goes between positive or negative and just add it the individual distances. Or when the sorry, when the when it's okay. No, when it's instantaneously at rest, you want to use those times. Okay. So t equals t and t equals four. Okay 60 zero smaller than t smaller than two than two to four and then it's greater than four. This point. Sleep cosive. 15 two. This one. 284. Two equal 16, 72, 96. 40 and. Then that's four. What is it before 64? 6416. Four. 嗯。And this. One then it's five greater than four is five 125. 25. Five. 42 24 is 40-32. 40 plus eight. 13. Get an answer for question nine. So 99A T equals two and t equals four. Yeah nine b is 56m. Yeah, perfect. That's looking great. Let's wrap it up there. But I think you've made a good start and a good den on variable acceleration. We'll finish it there and we'll catch up later. Okay. All right. Thank you, sir. Okay, see you later. Bye bye. Happy New Year. Bye you two. Bye, bye, bye.