An object moves in a straight line so that its position (in meters) as a function of…
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
An object moves in a straight line so that its position x (in meters) as a function of time t (in seconds) is given by
x=4.2t2.
You are interested in the object’s velocity at t=1.000s. Without using any calculus techniques, answer the following.
(a) Compute the object’s average velocity over the interval from 1.000 s to 1.010 s.
(b) Compute the object’s average velocity over the interval from 1.000 s to 1.001 s.
(c) Based on your calculations, provide your best numerical estimate (with units) of the object’s velocity at exactly 1.000 s. Explain why one of the two intervals yields a more accurate estimate than the other.