Find the Average and Instantaneous Velocity for s(t) = 4t^3

Math Problem Statement

The position of an object moving along a straight line after t seconds is modeled by the functions s(t)=4t^3-3 . Find the average velocity of the object over the following time intervals:
[2,2.1], [2,2.01] , [2,2.001] , and [2,2.0001] . Use the calculated averages to estimate the instantaneous velocity vinst of the object at t=2 seconds.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Instantaneous Velocity
Average Velocity
Limits

Formulas

Average velocity formula: v_avg = (s(t2) - s(t1)) / (t2 - t1)
Position function: s(t) = 4t^3 - 3

Theorems

Definition of Derivative
Limit Theorem

Suitable Grade Level

Grades 11-12 (Calculus)

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