Problem 1
Question
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 \(t=b ?\)
Step-by-Step Solution
Verified Answer
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 \(t \geq 0\).
1Step 1: 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 \(t=b\).
2Step 2: Calculate the change in position
The change in position is simply the difference between the positions at times \(t=a\) and \(t=b\), or \(s(b) - s(a)\).
3Step 3: Calculate the change in time
The change in time between \(t=a\) and \(t=b\) is the difference between the times: \(b - a\).
4Step 4: 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 = \(\frac{s(b) - s(a)}{b-a}\)
Other exercises in this chapter
Problem 1
Use a graph to explain the meaning of \(\lim _{x \rightarrow a^{+}} f(x)=-\infty\)
View solution Problem 1
Which of the following functions are continuous for all values in their domain? Justify your answers. a. \(a(t)=\) altitude of a skydiver \(t\) seconds after ju
View solution Problem 2
What is a horizontal asymptote?
View solution Problem 2
How are \(\lim _{x \rightarrow a^{+}} f(x)\) and \(\lim _{x \rightarrow a^{+}} f(x)\) calculated if \(f\) is a polynomial function?
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