The graph of \( s = f(t) \) represents the position of an object moving along a line at time \( t \geq 0 \).**Instructions:**1. **Assume the velocity of the object is 0 when \( t = 0 \). For what other values of \( t \) is the velocity of the object zero?**2. **When is the object moving in the positive direction and when is it moving in the negative direction?**3. **Sketch a graph of the velocity function.**4. **On what intervals is the speed increasing?****Diagram Explanation:**- The given image includes a graph showing the position \( s \) versus time \( t \). The \( t \)-axis ranges from 0 to 5, and the \( s \)-axis represents position.**Question Breakdown:**1. **Question a:** - The velocity of the object is zero at \( t = \) [_____] - *(Use a comma to separate answers as needed.)* 2. **Question b:** - When is the object moving in the positive direction? Select the correct choice below and, if necessary, fill in the answer box within your choice. - \( \circ \) A: The object is moving in the positive direction on the interval(s) [______]. - *(Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a comma to separate answers as needed. Use integers or decimals for any numbers in the expression.)* - \( \circ \) B: The object is never moving in the positive direction. - When is the object moving in the negative direction? Select the correct choice below and, if necessary, fill in the answer box within your choice. - \( \circ \) A: The object is moving in the negative direction on the interval(s) [______]. - *(Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a comma to separate answers as needed. Use integers or decimals for any numbers in the expression.)* - \( \circ \) B: The object is never moving in the negative direction.This content can help students understand the changing position of an object over time, specifically focusing on when the object's velocity is zero and when it is moving in positive or negative directions. It also ---**Understanding Velocity Functions and Graphs****Exercise: Sketch a Graph of the Velocity Function. Choose the Correct Graph Below.**You are presented with four options labeled A, B, C, and D. Each option provides a graph of velocity \( v \) as a function of time \( t \). Your task is to choose the correct graph based on given velocity data.- **Option A:** The graph shows an initial velocity decrease, followed by a gradual increase after \( t = 2 \), before leveling off.- **Option B:** The graph depicts an initial decrease in velocity, a small rise, and then a sharp decrease after \( t = 4 \).- **Option C:** This graph starts with a decrease, shows a point of inflection at \( t = 2 \), and then increases sharply after \( t = 4 \).- **Option D:** This graph indicates a steep decrease in velocity followed by a more gradual decrease that approaches zero.**Choosing the Right Interval:****Question: Select the correct choice below and, if necessary, fill in the answer box within your choice.**- **Option A:** The speed of the object is increasing on the interval(s) \[Blank Space\].(Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a comma to separate answers as needed. Use integers or decimals for any numbers in the expression. Use ascending order.)- **Option B:** The speed of the object never increases.**Detailed Analysis:**1. **Option A (Leading to an Increase in Speed):** Check the graph for intervals where the slope of the velocity function is positive (indicating acceleration or increasing speed).2. **Option B (Constant or Decreasing Speed):** Analyze if the graph shows no intervals with a positive slope, indicating the speed never increases.By interpreting the velocity graphs accurately, you can identify intervals where the object speeds up or ascertain if it maintains or reduces speed throughout.---This detailed transcription will help students understand how to analyze velocity functions graphically and identify intervals of increasing speed.

Answered: Image /qna-images/answer/7f6a49d0-1dfe-4ef8-9798-fbe1d9ed7f4d.jpg

The graph of s = f(t) represents the position of an object moving along a line at time t≥ 0. a. Assume the velocity of the object is 0 when t= 0. For what other values of t is the velocity of the object zero? b. When is the object moving in the positive direction and when is it moving in the negative direction? c. Sketch a graph of the velocity function. d. On what intervals is the speed increasing? a. The velocity of the object is zero at t=. (Use a comma to separate answers as needed.) b. When is the object moving in the positive direction? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The object is moving in the positive direction on the interval(s) (Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a comma to separate answers as needed. Use integers or decimals for any numbers in the expression.) OB. The object is never moving in the positive direction. When is the object moving in the negative direction? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The object is moving in the negative direction on the interval(s) (Simplify your answer. Type your answer in interval notation. Round to the nearest grid line as needed. Use a comma to separate answers as needed. Use integers or decimals for any numbers in the expression.) OB. The object is never moving in the negative direction. OON

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.CR: Chapter 4 Review

Problem 2CR: Determine whether each of the following statements is true or false, and explain why. The derivative...