in this video we'll be talking about the average acceleration and the instantaneous acceleration and we'll also be given example to differentiate between the average acceleration and the instantaneous acceleration so what is the average acceleration the average acceleration is denoted by a bar and then it is defined as the change in velocity in a given interval of time or in other words the final velocity minus initial velocity will give you the change in velocity and then the final time minus initial time so this is the formula for calculating the average acceleration the final velocity minus initial velocity divided by the final time once in some time the average acceleration is a vector quantity that means it does have both magnitude and direction the unit of the acceleration whether it is an average expression or the instantaneous acceleration the unit is meter per second squared and one thing to make a note is the average acceleration is always measured between the two times it is not measured at one time it is measured at in between the two times and as I already mentioned it is a vector quantity now let's talk about the instantaneous acceleration the instantaneous acceleration is the acceleration at one particular time or one particular position so it is at one particular time well and the average acceleration as I mentioned before it is measured between the two times between the two times where the instantaneous acceleration is measured at one time so how do you measure it in order to measure it we need to take the time derivative of the velocity or the first derivative of the velocity with respect to the time so that's how we measure it the this is the instantaneous acceleration and it is measured at the change a rate of change of velocity with respect to the time or the second derivative of the position also gives you the instantaneous acceleration all right so and again it is a vector quantity and the unit is meter per second square now let me give you an example to make a differences between the average velocity and the instantaneous average acceleration and the instantaneous acceleration let's say car is moving and the velocity of the car is changing with respect to the time and it is changing by this formula here VT is equal to 5 minus 10 T if that is the case then what is the average acceleration between the two time intervals between the 12 to 2 seconds and the time this is five second not the 50 seconds I'll just make one minor correction correctly this is the time is measured between the time to second and five second all right and okay and then we have also had to find out the instantaneous acceleration between those interim between at the two times 10 T equals to 2 second and a 5 second so let's start with the average acceleration now so the velocity is given then we need to find out the final velocity or the velocity at the time equals to 5 second so just plug in the v equals 2 time goes to 5 into this equation what I get is 5 minus 10 times 5 and it will V minus 45 meter per second that's the velocity at 5 second then we also calculate the velocity at 2 second which will be 5 minus 10 times 2 and it will be minus 15 meter per second and by the definition the average velocity which is denoted by a bar is the final velocity which is the velocity the velocity at 5 second minus the velocity the initial velocity at once Asad to second divided by the time the final time no let me okay the time at 5 second and the time for the let me write down in a different way okay the whale just write down the final velocity minus initial velocity minus the final time minus initial time the final velocity is the velocity at time T equals to five second which is minus 45 minus and the initial velocity is this time at the time it was two two second which is minus fifteen the final time this time is five second and the initial time is two second so what you get is a minus 40 plus 15 divided by three which you get minus 30 divided by three and it is equal to minus 10 and the unit is meter per second square so that is the average acceleration to minus 10 meter per second square is the average expression now let's calculate the instantaneous acceleration the instantaneous acceleration is it is defined by a equals to DV t / DT that is the first derivative of the velocity if we take the first derivative it's a constant the v is a constant term so it'll be 0 and if I take 10 T it'll be negative 10 so the number is negative 10 meter per second squared so this is the instantaneous acceleration and you see it is not dependent on the time so it is so this one is not dependent on the time because it does not have any time term so the instant an instantaneous acceleration at the time not all times is exactly the same a time goes to plus a two-second it is minus 10 meter per second square and also at time equals to 5 second it is a still 10 meter per second square okay now let me give you another example of the the differences between the average and the instantaneous acceleration now let's suppose this is the example number 2 now now let's suppose the velocity is 5 minus 10 T Square and now we're going to find out the average acceleration and instantaneous acceleration at time equals to two second and time it goes to five second and between these two time intervals we're going to find out the average acceleration so again we need to find out the velocity at that time goes to two second and this can be given by ten times to a square so it is 40 minus five you'll get minus 35 meter per second and now velocity at five second it will be able 5 minus 10 times 5 square so 250 minus five it will be negative 245 meter per second so the average acceleration which is the final velocity minus initial velocity divided by final time I will just write down at the bottom okay so so average acceleration is final velocity minus initial velocity divided by the final time minus initial time what is the final velocity the final velocity is the velocity at time cos two five second which is minus 245 - an initial velocity is 35 the time is it five second - two second so if we do the math what we get 245 - 35 200 about three we'll get 70 so the answer is minus 70 meter per second squared thus the average acceleration between time T goes to 5 second and time equals to 2 seconds so this is the average acceleration now let's calculate the instantaneous acceleration okay the instantaneous acceleration is defined as d the first derivative of the velocity ok and what is the velocity the velocity is given by v minus 10t squared that's how the velocity is given 5 minus 10 t is squared if I just take a derivative it's a constant on 5 is a constant term so you'll get 0 minus 10 times 2t we'll get negative 20 T but now let's put at the different times now the time equals to 2 second will get minus 20 times 2 and this will be minus 40 meter per second square and now at time T equals to 5 second it'll minus 20 times 5 which will be minus 100 meter per second square so you see now the average acceleration between the time between the time 5 second and the 2 second we get minus 70 meter per second square and this is the instantaneous acceleration in staunton this expression that the two times is different one is a minus 40 and the other is minus 100 so these are the instantaneous acceleration okay so this is how we calculate the average acceleration and the instantaneous acceleration I hope this one helps you to understand the differences between the average acceleration and the instantaneous acceleration