MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A particle moves along a straight line. Its position at time t seconds is given by
s(t)=t3−6t2+9t metres.
Answer the following questions.
(a) Write an expression for the average velocity of the particle over the interval [2,2+h], where h=0.
(b) Simplify the expression obtained in part (a) to obtain vavg(h) solely in terms of h.
(c) Evaluate h→0limvavg(h).
(d) Interpret the physical meaning of the limit calculated in part (c) and state its numerical value with proper units.