in this video we're going to talk about acceleration but before we do that let's talk about the difference between velocity and acceleration both quantities are vectors they both have magnitude and Direction but what is the difference between velocity and acceleration velocity tells you how fast an object's position is changing with respect to time so basically velocity is the displacement which is the change in position over time so V is equal to the displacement is the final position minus the initial position divided by the elapse time now as T approaches zero this expression is or becomes rather the instantaneous velocity the previous equation represents the average velocity so if you want to find the average velocity simply use this equation it's the position I mean it's the change in position over time or displacement over time so that will give you the average velocity whereas the instantaneous velocity you can use the same formula but when T becomes very very small it will give you the instantaneous velocity now let's say if you have a car that's moving at 30 m hour traveling East so this expression the magnitude and the direction that represents the velocity of the vehicle so every hour the car travels a distance of 30 mil so in 2 hours it's going to travel 60 mil 3 hours 90 mil so speed tells you how fast the distance is changing velocity tells you how fast the displacement is changing so let's say if a car or let's say if an object's moving at a speed of 8 m/ second every second the distance is changed by 8 m so after 1 second the distance travel is 8 m 2 seconds 60 m 3 seconds 24 M so that's the main concept between speed and velocity it tells you how fast the distance or the displacement is changing every second so if a car is moving at a speed of 15 m/ second every second the distance is changing by 15 M so to sum up what we just considered speed tells you how fast the distance is changing velocity tells you how fast the displacement is changing acceleration tells you how fast the velocity is changing so acceleration this is average acceleration it's equal to the change in velocity you say Delta V if you want to over time that'll give you the average acceleration if you want to find an instantaneous acceleration as T approaches zero when T becomes very small that is the change in time this expression will give you the instantaneous acceleration but if it's over a significant time interval then that equation will give you the average acceleration so just as speed tells you how fast the distance is changing acceleration tells you how fast the velocity is changing so let's say if the acceleration is 8 m/s squar so that means every second the velocity is changing by 8 m/s so in 1 second let's say let's make a table let's say this is time and velocity after 1 second the speed will be 8 m/s after 2 seconds the velocity will be 16 3 seconds 24 and then 4 seconds 32 so every second the velocity is increasing by eight so that's the main idea behind acceleration it tells you how fast the velocity is changing now starting from this equation there's another equation that you might find useful let's multiply both sides by T So a is equal to V final minus V initial now let's add V initial to both sides so V initial plus a t is equal to V final so anytime you want to calculate the final speed for motion or any object that's undergoing accelerated motion you can use this equation the acceleration has to be constant by the way for this to work so when an object is moving with constant acceleration you could find the final speed given the initial speed the acceleration and a time now let's work on some problems a car accelerates from 15 m/s to 45 meters per second in 5 seconds calculate the average acceleration of the car now what I like to do is I like to make a list of what I have and what I need to find so the initial speed in this problem is 15 m/ second the car accelerates from that speed to a final speed of 45 m/ second the time in between those two points is 5 Seconds our goal is to calc calculate the average acceleration so the formula that we could use is this one acceleration is equal to V final minus V initial / T the final speed is 45 the initial speed is 15 and a time is five so the change in speed is 30 m/s and we're going to divide that by 5 Seconds 30 / 5 is 6 so the acceleration is 6 m/s squared now let's understand this problem so let's make a table so this is the acceleration let's make a table between time and velocity at T equals 0 the initial speed is 15 m/s now keep in mind the acceleration tells us how much the speed changes or the velocity changes every second so 1 second later it's going to be 6 m/ second higher so 15 + 6 is 21 whenever the acceleration is positive the velocity is increasing 2 seconds later it's going to be at 27 so every second the speed is going to increase by 6 m/s so at 3 seconds it's going to be 33 and at 4 seconds it's going to be 39 and 5 seconds later it's going to reach to our final speed of 45 m per second so I want you to understand the concept of acceleration and just think of it as how fast the speed changes or how fast the velocity changes every second number two a truck accelerates from 25 km per hour to 45 km/ hour in 40 seconds calculate the average acceleration of the vehicle in kilm hour per second and in meters per second second squ so go ahead and take a minute and work on this problem so just like before we're going to make a list of what we have and what we need to find so what does the 25 kilm per hour uh value represent so that is the initial speed of the vehicle now we know that the final speed has to be 45 km per hour and the time in between these two events is 40 seconds so now we could use the same formula to calculate the average acceleration so the average acceleration is the change in the velocity divided by the time the final speed is 45 the initial speed is 25 and the time is 40 so 45 minus 25 that gives us a change of 20 20 and a unit is KM hour and let's divide that by 40 seconds well 20 / 40 is the same as 2 / 4 which is 12 or .5 now notice what the units for this acceleration will be we have kilomet hours ided by seconds so the units is going to be kilom per hour per second so that's our answer that's the acceleration now let's focus on the second part of the problem we need to convert this unit to m/s squar which is the most common unit you'll see for acceleration so how should we Rite this on the first fraction five has to go on top and kilm it's .5 km per hour per second so the second two units have to go in the bottom now what we need to do is change kilometers to meters 1 kilm is equivalent to 1,000 M and we need to write it in such a way so that the unit kilm will cancel now all we need to do is convert this hour into 2 seconds so 1 hour is equal to 60 minutes and 1 minute is equivalent to 60 seconds so the unit hours cancel and the unit minutes cancel so now we have meters per second per second or m/s squared 5 * 1,000 is 500 and we're going to divide that by 60 which is about 8 33 and divide that by 60 again so the acceleration of this vehicle is.3 8 repeating m/s squared so that's the answer so make sure you know how to convert from oneit of acceleration into another here's another problem that we can work on a car accelerates from rest at a constant rate of 3.5 m per second squared what is the speed of the car 12 seconds later so pause the video and work on this problem see if you can find an answer now what variables do we have in this problem what is the initial speed and what is the final speed what is the time and what is the acceleration as well now whenever you hear the word rest that tells you that the speed is zero the car accelerates from rest that means it's accelerating from an an initial speed of zero our goal is to find the final speed of the vehicle so that's what we're looking for the time is 12 seconds and the acceleration is 3.5 m/s squ so what equation do we need to use in order to calculate the final speed so we need to use this formula the final speed is equal to the initial speed plus the product of the acceleration and a Time the initial speed is zero the acceleration is 3.5 and the time is 12 so all you need to do is multiply 3.5 * 12 and that will give you the final speed of 42 m/s number four a bus accelerates from an initial speed of 12 m/s at a constant rate of 1.2 m/s squared what is the final speed of the bus after 15 seconds so just like before let's make a list of the variables that we have and a variable that we need to find so we're given the initial speed which is 12 m/s and looking at the units m/s squared we can see that that value represents the acceleration and if you see the unit seconds you know that represents time our goal is to find the final speed of the bus so we need to calculate VF therefore we can use the same exact equation as the one we used in the last problem so VF is equal to V initial + 18 the initial speed is 12 the acceleration is 1.2 and the time is 15 seconds so first let's multiply 1.2 by 15 1.2 * 15 is 18 and 12 + 18 is 30 so the final speed is 30 meters per second number five a sports car driver traveling at 95 milph slams the brakes and comes to rest in 4 seconds calculate the average acceleration of the car in me/ second squ so let's think about this if we want to find the acceleration in m/s square we need to convert the speed from Miles hour to me/ second is not like the second problem where we had to get the answer in terms of kilm per hour per second if we only needed to get the answer in meters per second squar I would have changed the units from the beginning but in this case we need to get it in meters per second squar so let's begin by converting miles hour to me/ Second so we have 95 miles per hour 1 hour contains 60 minutes and each minute contains 60 seconds now how can we convert miles to meters one way we can do it is we can convert miles to kilom and then kilom to meters so we need to know the conversion if I recall 1 km is 6214 mil and we know that 1 kilomet is also 1,000 M so as we can see the unit miles cancels hours uh cancel as well the same is true for minutes and finally kilom so we're left with meters per second now let's do the math 95 ided by 60 divid by another 60 ID 6214 time 1,00 is about 42.4 47 so that's the initial speed of the vehicle it's 42.4 m/s now what is the final speed of the vehicle if the driver slams the brakes he's going to come to rest eventually so the final speed is zero the time we can see it's 4 seconds and our goal is to find the acceleration so let's use this formula a is equal to V final minus V initial / T so it's 0us 42.4 / 4 so - 42.4 ID 4 4 that's about -10.6 m/s s now why is the acceleration negative the speed is decreasing anytime the velocity is decreasing which is the magnitude of speed speed is the magnitude of velocity but anytime uh the velocity is decreasing the acceleration will be negative and car is slowing down it's coming to a stop and so that's why you should have a negative average acceleration so that's what it means