Math Problem Statement

Suppose that an object is moving along a vertical line. Its vertical position is given by the equation , where distance is measured in meters and time in seconds. Find the approximate value of the average velocity (accurate up to three or more decimal places) in the given time intervals.

Solution

To find the average velocity of the object over a given time interval, we use the formula for average velocity:

vavg=s(t2)s(t1)t2t1v_{\text{avg}} = \frac{s(t_2) - s(t_1)}{t_2 - t_1}

where s(t)s(t) is the position function, t1t_1 is the start time, and t2t_2 is the end time.

Could you please provide:

  1. The position function s(t)s(t).
  2. The specific time intervals [t1,t2][t_1, t_2].

With this information, I can calculate the average velocity accurately.

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Math Problem Analysis

Mathematical Concepts

Average Velocity
Position Function
Rate of Change

Formulas

v_avg = (s(t2) - s(t1)) / (t2 - t1)

Theorems

Definition of Average Velocity

Suitable Grade Level

Grades 10-12