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Chapter 2: Problem 1

Suppose \(s(t)\) is the position of an object moving along a line at time \(t \geq 0 .\) What is the average velocity between the times \(t=a\) and \(t=b ?\)

Short Answer

Expert verified
Answer: The formula to calculate the average velocity is: Average velocity = \(\frac{s(b) - s(a)}{b-a}\), where \(s(t)\) represents the position of the object at any time \(t \geq 0\).

Step by step solution

01

Identify the given information

We are given that \(s(t)\) represents the position of the object at any time \(t \geq 0\). We need to find the average velocity between the times \(t=a\) and \(t=b\).
02

Calculate the change in position

The change in position is simply the difference between the positions at times \(t=a\) and \(t=b\), or \(s(b) - s(a)\).
03

Calculate the change in time

The change in time between \(t=a\) and \(t=b\) is the difference between the times: \(b - a\).
04

Find the average velocity

We can now find the average velocity by dividing the change in position by the change in time, as follows: Average velocity = \(\frac{s(b) - s(a)}{b-a}\)

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