in this video we'll be talking about the graphical analysis of average acceleration and instantaneous acceleration listen we have a graph here this is the time axis this is the time axis and this is the velocity and the velocity varies as given by this equation here this is how does the velocity vary at the starting time but said this is the starting time TI is the initial time at this point the starting point the object started with the velocity VI and after time T F the the final velocity of the particle is V F and we need to find out what is the average acceleration between these two times these two times how do we do that in order to find the average acceleration between these two times graphically we just need to connect the initial point and the final point I'm making it a different color so I just connected the initial point and the final point the initial and the final point the slope of this line gives the average acceleration if it just measure the slope of this line that gives you the average acceleration and how to measure the slope of this line in order to measure the slope how the slope is defined it is defined as the rise over run so in this case in this case the average acceleration would be this value the change in the velocity the final velocity is VF and the initial velocity is V I so the change in the velocity between these two times is VF minus VI divided by TF minus TI that gives you the average acceleration now how do I find out the the instantaneous acceleration the instantaneous acceleration let's say at this point is if I draw if I draw tangent at this point I'll just use a different color disco so if we draw a tangent at this point that's the slope of this tangent it gives you the the slope of this tangent gives you the instantaneous acceleration similarly if I draw a tangent at this point then when the slope of these lines gives you d the instantaneous acceleration okay so this is how you find the average acceleration and the instantaneous acceleration