The coordinates of s of a moving body for various values of t are given (a) F(sec) 0 0.5 1.0 | 1.5 | 2.0 | 2.5| 3.O | 3.5|4.0 s (1) -12 -15–16 –15 –12 –7 09 20 (a) Plot s versus 1, and sketch a smooth curve through the given points. (b) Assuming this smooth curve represents the motion of the body, estimate the velocity at t = 1.0, t = 2.5, and t = 3.5. (0, 4] by l-20, 201 (b) t = 1.0: t = 2.5: 1= 3.5:
The coordinates of s of a moving body for various values of t are given (a) F(sec) 0 0.5 1.0 | 1.5 | 2.0 | 2.5| 3.O | 3.5|4.0 s (1) -12 -15–16 –15 –12 –7 09 20 (a) Plot s versus 1, and sketch a smooth curve through the given points. (b) Assuming this smooth curve represents the motion of the body, estimate the velocity at t = 1.0, t = 2.5, and t = 3.5. (0, 4] by l-20, 201 (b) t = 1.0: t = 2.5: 1= 3.5:
College Physics
11th Edition
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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S versus T graph and velocity of a moving body.
![**Educational Content: Analysis of Motion Using Coordinates**
The coordinates \( s \) of a moving body for various values of \( t \) (time in seconds) are given in the table below:
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
t \, (\text{sec}) & 0.0 & 0.5 & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 & 3.5 & 4.0 \\
\hline
s \, (\text{ft}) & -12 & -15 & -16 & -15 & -12 & -7 & 0 & 9 & 20 \\
\hline
\end{array}
\]
**Tasks:**
(a) **Graphical Analysis**
- Plot the values of \( s \) (in feet) against \( t \) (in seconds) on a graph.
- Sketch a smooth curve that passes through these points to visualize the motion of the body.
The provided diagram (referenced as (a) in the image) represents an empty graph template with a range from \( [0, 4] \) on the x-axis (time) and from \([-20, 20]\) on the y-axis (position).
(b) **Velocity Estimation**
- Assuming the smooth curve you drew represents the motion of the body, estimate the velocity at specific time points: \( t = 1.0 \), \( t = 2.5 \), and \( t = 3.5 \).
Fill in the blanks:
- \( t = 1.0: \) ________________
- \( t = 2.5: \) ________________
- \( t = 3.5: \) ________________
**Instructions for Estimation:**
1. **Understand the Graph**: Analyze the slope of the tangent at each of the given time points to determine the velocity.
2. **Calculate Velocity**: Since velocity is the rate of change of position with respect to time, approximate this by examining the change in \( s \) over a small interval around each \( t \) value.
This exercise provides a practical application for understanding motion, graph interpretation, and instantaneous velocity estimation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b2fbfa8-0fc4-4bf7-b479-8ac42dd1f210%2F26683ef8-9448-41fc-ad43-efb9c5c37a12%2F595wq7r_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Analysis of Motion Using Coordinates**
The coordinates \( s \) of a moving body for various values of \( t \) (time in seconds) are given in the table below:
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
t \, (\text{sec}) & 0.0 & 0.5 & 1.0 & 1.5 & 2.0 & 2.5 & 3.0 & 3.5 & 4.0 \\
\hline
s \, (\text{ft}) & -12 & -15 & -16 & -15 & -12 & -7 & 0 & 9 & 20 \\
\hline
\end{array}
\]
**Tasks:**
(a) **Graphical Analysis**
- Plot the values of \( s \) (in feet) against \( t \) (in seconds) on a graph.
- Sketch a smooth curve that passes through these points to visualize the motion of the body.
The provided diagram (referenced as (a) in the image) represents an empty graph template with a range from \( [0, 4] \) on the x-axis (time) and from \([-20, 20]\) on the y-axis (position).
(b) **Velocity Estimation**
- Assuming the smooth curve you drew represents the motion of the body, estimate the velocity at specific time points: \( t = 1.0 \), \( t = 2.5 \), and \( t = 3.5 \).
Fill in the blanks:
- \( t = 1.0: \) ________________
- \( t = 2.5: \) ________________
- \( t = 3.5: \) ________________
**Instructions for Estimation:**
1. **Understand the Graph**: Analyze the slope of the tangent at each of the given time points to determine the velocity.
2. **Calculate Velocity**: Since velocity is the rate of change of position with respect to time, approximate this by examining the change in \( s \) over a small interval around each \( t \) value.
This exercise provides a practical application for understanding motion, graph interpretation, and instantaneous velocity estimation.
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