robphy said:Let v1=At for a time t1
then v2=Bt+At_1 for an additional time t2.
Then a1=A and a2=B.
However, the [time-weighted] average acceleration is
aavg= (a1t1+a2t2)/(t1+t2)=(At1+Bt2)/(t1+t2).
Average acceleration is the change in velocity divided by the time it takes for that change to occur. It represents the average rate at which an object's velocity changes over a certain period of time.
Instantaneous acceleration is the acceleration at a specific point in time, or at a specific instant. It is calculated by taking the limit as the time interval approaches zero in the equation for average acceleration.
The main difference between average and instantaneous acceleration is that average acceleration represents the change in velocity over a certain period of time, while instantaneous acceleration represents the acceleration at a specific instant in time.
Some examples of average acceleration include a car accelerating from 0 to 60 miles per hour in 5 seconds, a roller coaster accelerating downward at a constant rate, or a plane speeding up during takeoff.
Average acceleration is calculated by dividing the change in velocity by the time it takes for that change to occur. The equation for average acceleration is a = (vf - vi) / t, where vf is the final velocity, vi is the initial velocity, and t is the time interval.