Average and Instantaneous Velocity

[dmonlama]

Homework Statement

a. Show that if the position x of a moving point is given by a quadradic function of t,x = At^2 + Bt + C, then the average velocity over any time iunterval [t1,t2] is equal to the instantaneous velocity at the midpoint of the time interval.
b. What is the geometric significance of the result in part (a)?

 

[CompuChip]

How do you calculate the average velocity over a given interval?
How do you calculate the instantaneous velocity at a given moment?
Can you give us the formulas?