and this video will be talking about the difference between the average velocity and the instantaneous velocity the evidence velocity is the total the displacement divided by the time so let's first calculate the average velocity average velocity in order to calculate the average velocity you need to know the initial position and the final position here it is asking you to calculate the average velocity between the time one second and the time five second so in order to know or calculate the average velocity between these two time you need to know the position of the object at this time what is the position at time T equals to one second and what is the position at time T equals to five second so we can calculate so the the position as a function of time is given which is two minus 5t plus 3t squared so I can calculate the position at the two times time goes to one second so two two minus five times 1 + 3 3 times 1 square so if you calculate what I get is a so the I will get zero meters at the time cheapest once again the position was at origin zero meter in the same way I can calculate the position at time goes to 5 second and thus plugging time because - five seconds into this equation 2 minus 5 times 5 plus 3 times five is square 5 squared is 25 times 375 minus 25 50 that's 2 it'll it will give you 50 2 meter 52 meter so this is the final position this is the final position and this is the initial position so the average velocity has a velocity it's denoted by the bar and it is defined as the final position minus the initial position divided by the final time 1 is the initial time the final position is 52 meter and the initial position is 0 meter the final time is 5 minus 1 and if we do the math you'll get 13 point 5 meter per second that is the average velocity now let's calculate the instantaneous velocity with instantaneous velocity is given by the rate of change of position that means T XT or DT that's that gives you the instantaneous velocity sold so D we had to do the first derivative or the position which is now 2 minus 5t + 3 T Square so this is a constant - is a constant so if I take a time derivative it'll be 0-5 and it will be 6 times T if you want to know how to take the time derivative please watch my other videos how to do the the derivatives so what I get is minus 5 plus 6 times T this is the VT or instantaneous velocity now what is asking here find the cars instantaneous velocity at time T equals to one second and time T equals to 5 second so how do we find out the instantaneous velocity in one second v1 just plugging into this equation minus five minus five plus six she'll get one meter per second so the time equals to one second it was moving at that moving with one meter per second and now at the time T equals to five second minus 5 plus 6 times 5 30 minus 5 is 25 meter per second now in five set of time goes to five second it is moving at 25 meter per second so the particle has accelerated but now this is how do you calculate the average velocity and instantaneous velocity again in order to calculate the average velocity in order to calculate the average velocity you need to know the position your initial push your initial position and the final position and then the then you calculate the displacement by final by calculating final position minus initial position but in order to calculate the instantaneous velocity you take the time derivative that's how you calculate the instantaneous velocity and the average velocity