Difference quotient
In physics, the instantaneous velocity of an object (the velocity at an instance in time) is defined as the derivative of the position of the object (as function of time). For example, if an object's position is given by x(t)=-16t2+16t+32, then the object's velocity is v(t)=-32t+16. To find the instantaneous acceleration, one simply takes the derivative of the instantaneous velocity function. For example, in the above function, the acceleration function is a(t) = -32.