7) An object in free fall has its distance from the ground measured by the function d(t) = -4.9t² + 50, where d is in meters and t is in seconds. If gravity is the only acceleration affecting the object, what is gravity's constant value (include units in your answer)?
7) An object in free fall has its distance from the ground measured by the function d(t) = -4.9t² + 50, where d is in meters and t is in seconds. If gravity is the only acceleration affecting the object, what is gravity's constant value (include units in your answer)?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem 7: Analyzing Free Fall Motion**
An object in free fall has its distance from the ground measured by the function \( d(t) = -4.9t^2 + 50 \), where \( d \) is in meters and \( t \) is in seconds. If gravity is the only acceleration affecting the object, what is gravity’s constant value (include units in your answer)?
**Problem 8: Graphical Analysis and Sketching Derivatives**
The graph of \( y = f(x) \) is shown on the domain \([0, 5]\). Sketch the graph of \( y = f''(x) \) on the same domain.
**Graph Description:**
- It displays a curve starting at approximately (0, 1) and ends beyond (5, 7).
- The function decreases from (0, 1) to around (1, 0.5), where it reaches a minimum.
- Then it increases, reaching a local maximum around (2.5, 2.5).
- The curve then decreases slightly and continues to increase steeply toward the end of the domain at (5, 7).
When sketching \( y = f''(x) \):
- Focus on the concavity changes: intervals of concavity can be determined by observing where the derivative \( f'(x) \) has local extrema.
- Positive \( f''(x) \) indicates the curve is concave up, and negative \( f''(x) \) indicates concave down.
**Note to Users:**
The task is to analyze these details to understand the underlying patterns of free fall and the behavior of the graph function to their second derivatives, promoting deeper insights into calculus concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F883933e7-6864-477d-8bb2-712659e12b95%2F750ce03d-cbde-4bc9-a187-90ea582afe5e%2F024jxp_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 7: Analyzing Free Fall Motion**
An object in free fall has its distance from the ground measured by the function \( d(t) = -4.9t^2 + 50 \), where \( d \) is in meters and \( t \) is in seconds. If gravity is the only acceleration affecting the object, what is gravity’s constant value (include units in your answer)?
**Problem 8: Graphical Analysis and Sketching Derivatives**
The graph of \( y = f(x) \) is shown on the domain \([0, 5]\). Sketch the graph of \( y = f''(x) \) on the same domain.
**Graph Description:**
- It displays a curve starting at approximately (0, 1) and ends beyond (5, 7).
- The function decreases from (0, 1) to around (1, 0.5), where it reaches a minimum.
- Then it increases, reaching a local maximum around (2.5, 2.5).
- The curve then decreases slightly and continues to increase steeply toward the end of the domain at (5, 7).
When sketching \( y = f''(x) \):
- Focus on the concavity changes: intervals of concavity can be determined by observing where the derivative \( f'(x) \) has local extrema.
- Positive \( f''(x) \) indicates the curve is concave up, and negative \( f''(x) \) indicates concave down.
**Note to Users:**
The task is to analyze these details to understand the underlying patterns of free fall and the behavior of the graph function to their second derivatives, promoting deeper insights into calculus concepts.
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Question-7
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the given equation is
an object body is falling freely for time t seconds with initial velocity v0, from an initial height h0, due to gravity g.
It will follow the following equations of motion as
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