What is instantaneous acceleration?

The derivative of velocity with respect to time.
##a=(dv)/dt##
Imagine your your driving a car. As you accelerate you observe the needle of your speedometer moving smoothly from 0 to 60 miles an hour. What is your ?
By definition your acceleration is the rate of change in in your velocity within a particular amount of time.
##(v2-v1)/(t2-t1)##
If we take the limit at which the difference in time between ##t2## and ##t1## or ##trianglet## approaches zero we can find the time derivative of the the velocity which is the instantaneous acceleration.
##a = lim_(trianglet->0) (trianglev)/(trianglet)##