in this video we're going to talk about kinematics particularly the formulas that you'll be using when you're studying this chapter in physics kinematics has to do with motion this could be Motion in One Direction such as along the x-axis or Motion in two dimensions in that case that will be along the X and the y axis now one of the first Concepts that you need to be familiar with is something called displacement I'm just going to write D for displacement displacement along the x-axis is Delta X which is the change in position which is the final position minus the initial position along the x-axis now in addition to horizontal displacement you also have vertical displacement d y which is equal to Delta y and that is equal to the final position minus the initial position along the y-axis so that's displacement displacement is a vector distance is a scalar quantity displacement is basically you can think of distance but with Direction next we have velocity velocity is the rate of change of displacement with respect to time so it's D over t you can also use this formula to calculate velocity in the X Direction the change in X over the change in time so it's the change in position with respect to time or displacement over time you can also find velocity in the y direction as well now the difference between speed and velocity is that speed is the absolute value of velocity speed is a scalar quantity it only has magnitude only no Direction velocity is a vector quantity it has magnitude and Direction so velocity is speed with Direction speed can only be positive but velocity can be positive or negative distance the fact that it's a scalar quantity it can only be positive but displacement can be positive or negative because it's a vector quantity now just as velocity is the rate of change of displacement over time acceleration is the rate of change in velocity over time so it's Delta V over delta T so you can calculate velocity by taking the final position subtracting it by the initial position and dividing it by the time between or the time it takes to go from initial to final acceleration is very similar It's the final velocity minus the initial velocity divided by the time now I want to take a moment to show you where you can access more practice problems on kinematics so if you go to patreon.com maths science tutor you'll get access to my patreon page and when you sign up this is what it's going to look like now I do have a lot of subjects but let's focus on physics so if we click on physics you'll get access to my physics videos and the worksheets as well so you could start with this one distance and displacement I have 18 practice bombs on that so the worksheet has all the practice problems found in the video for those of you who want to print out of all the problems but this is the video I was talking about kinematics where if you want to put those formulas into use you can access the video here now if you go to YouTube you can access the free version which is about 31 minutes long so if you type in kinematics organic chemistry tutor that video should come up but on patreon the full version it's about an hour and 52 minutes long so you have way more content here along with the worksheet as well now if you were to click on this video and if you go to the description section below you could find the direct link that'll take you to the full version of the video on patreon and also the direct link that will take you to the worksheet now let's go back to my patreon page here's another video well that's a worksheet but here's another video that has more problems on kinematics this is kinematics but in the y direction Free Fall problems so you may want to take a look at that there's other physics videos like vectors projectile motion relative velocity and if you're taking a course on physics eventually you're gonna run into these topics like tension 4 static friction inclined planes pulleys work and energy impulse momentum you can find all of my extended videos on these topics here now in addition to that you'll be getting access to my physics final exam review video the free version on YouTube is about two hours long but the full version is six hours long with 100 practice problems and you can also get a printout of the problems as well for those of you who may want to study it in class as you can see there's a lot of questions on it so feel free to take a look at that when you get a chance now you can access many of my extended videos on my YouTube membership program but if you want access to the worksheets I only have that currently available on my patreon membership program so just something that you should know I'm going to post a few links in the description section below this video so feel free to take a look at that when you get a chance now let's talk about the difference between average velocity and instantaneous velocity as well as average acceleration and instantaneous acceleration so first let's start with average velocity the formulas that we've been talking about has to do with average velocity which is displacement over time or you could say x final minus X initial over t if you want to calculate the instantaneous velocity represented by V if you see a bar on top that means average velocity you need to use the limit function the limit as delta T approaches zero but for the same formula Delta X over delta T so let's say if you want to calculate the average velocity along a time interval of one to nine seconds or let's say two to eight or three to seven or four to six notice the change in time here it's 8. here the change in time is six the change in time here is 4. and delta T is 2. if you were to average one and nine you get five if you were to average two and eight you would get five the same is true four the remaining numbers so all of these intervals what they can allow you to do is they can allow you to estimate the instantaneous velocity when T is five because 5 is the average of each pair of numbers in those intervals now as delta T gets smaller as you go from a to 2 this formula becomes a better estimate of the instantaneous velocity the closer you get to zero you can use this formula to approximate the instantaneous velocity the average velocity gets closer and closer to the instantaneous velocity as delta T approaches zero so let's say if we're to use an interval of 4.9 the 5.1 with 5 being the center delta T in this case is 0.2 now if we were to use an interval like 4.99 and 5.01 delta T is very close to zero it's .02 . so if you were to use these numbers using the average velocity formula it would give you a very good approximation of the instantaneous velocity because delta T is getting closer and closer to zero so that's how you can use that formula to approximate the instantaneous velocity it's by using limits and making the interval small as possible getting close to this number or the number you want to find the instantaneous velocity at now if you want to calculate the average acceleration you could use this formula is the change in velocity over the change in time if you want to calculate the instantaneous acceleration is the limit as delta T approaches zero but for the same formula Delta V over delta T the only difference here is you want to make delta T very small such that it's close to zero so for instance let's say if you want to calculate the instantaneous acceleration at T equals seven so if you were to use 6.9 and 7.1 that will give you a good approximation if you were to use 6.99 and 7.01 as T initial T and final that will be an even better approximation so the closer and closer delta T gets to zero the better the approximation another formula that you're going to see in kinematics is displacement is equal to V initial the initial velocity multiplied by the time plus one half a t squared now if you're wondering where this portion of the formula comes from it's from this D is equal to VT remember that we said velocity is displacement over time if you multiply both sides by time you get displacement is velocity multiplied by time now this equation works if you have constant velocity if you have constant acceleration then this formula applies for constant acceleration you have a variation of this formula so instead of V you would use the average velocity for constant acceleration where the average is going to be the sum of the initial and the final velocity divided by 2. so here's two common kinematic formulas that you need to be familiar with now we said that acceleration is the change in velocity over time and Delta V is V final minus V initial if we multiply both sides by T we get this and if we add the initial to both sides we get V initial plus a t is equal to VF so here's another kinematic formula that you need to be familiar with v final is equal to V initial plus a t now the last commonly used kinematic formula is this one V final squared is equal to V initial squared plus two a d but here's a question for you where does this formula come from how can we derive that formula what would you say what would you do to derive that formula it turns out that we could use this equation and this one to get this formula so what I'm going to do is I'm going to rearrange this equation to get t so I'm going to multiply both sides by T these will cancel I get a t is equal to V final minus V initial and then I'm going to divide by a so we have t is equal to V final minus phen is shown over a now starting with this formula I'm going to replace t with what I have here so I'm going to have D is equal to one half V initial plus the V final times V final minus V initial over a now I'm going to multiply both sides of the equation by 2A so on the left I have 2ad on the right the 2 is going to cancel with the one-half and a will cancel so now I can foil those two binomials so I have V initial times the V final and then V initial times the negative V initial that's negative Phi initial squared and then V final times the V final that's positive V final squared and then V final times negative V initial I'm going to put it right here because these two will cancel and I'm low on space so bringing everything down we have 2ad is equal to I'm going to write this one first so V final squared and then minus it has a negative so minus V initial squared now I'm going to add the initial Square to both sides so I get V initial squared Plus 2ad is equal to V final squared so that's how you could derive that formula from two other kinematics formula so using those two previous kinematic formulas we're able to get that one V final squared is equal to V initial squared plus two a d so that's basically it for this video for those of you who want practice problems on kinematics feel free to check out the links in the description section below this video or you can type in kinematics organic chemistry tutor in a YouTube search box and you'll get a video that will give you problems on how to use these formulas