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Sagot :
To properly address the given problem, we shall first construct the position-time graph by plotting the provided data points [tex]\((T, X)\)[/tex]:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline T (s) & 0 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 90 & 95 & 50 \\ \hline X (m) & 5 & 10 & 15 & 25 & 35 & 50 & 60 & 65 & 70 & 73 & 75 \\ \hline \end{array} \][/tex]
### 1. Plotting the Position-Time Graph
To draw the graph, follow these steps:
1. On the x-axis, plot the time (T) in seconds.
2. On the y-axis, plot the position (X) in meters.
3. Mark the coordinates corresponding to each time and position pair.
4. Connect the points to visualize the motion.
### 2. Analysing Motion and its Features
Let's observe the data and the plot we would create:
#### Feature 1: Initial Velocity
- From [tex]\(T = 0\)[/tex] to [tex]\(T = 5\)[/tex]:
[tex]\[ v_1 = \frac{X(5) - X(0)}{T(5) - T(0)} = \frac{10 - 5}{5 - 0} = \frac{5}{5} = 1 \text{ m/s} \][/tex]
#### Feature 2: Consistent Speed Intervals
- From [tex]\(T = 5\)[/tex] to [tex]\(T = 10\)[/tex]:
[tex]\[ v_2 = \frac{X(10) - X(5)}{T(10) - T(5)} = \frac{15 - 10}{10 - 5} = \frac{5}{5} = 1 \text{ m/s} \][/tex]
- From [tex]\(T = 10\)[/tex] to [tex]\(T = 15\)[/tex]:
[tex]\[ v_3 = \frac{X(15) - X(10)}{T(15) - T(10)} = \frac{25 - 15}{15 - 10} = \frac{10}{5} = 2 \text{ m/s} \][/tex]
#### Feature 3: Accelerated Motion
From [tex]\(T = 15\)[/tex] to [tex]\(T = 20\)[/tex], [tex]\(T = 25\)[/tex], etc., the velocity can be observed to change significantly, suggesting acceleration:
- From [tex]\(T = 15\)[/tex] to [tex]\(T = 20\)[/tex]:
[tex]\[ v_4 = \frac{X(20) - X(15)}{T(20) - T(15)} = \frac{35 - 25}{20 - 15} = \frac{10}{5} = 2 \text{ m/s} \][/tex]
- Continued calculation for each segment up to [tex]\(T = 35\)[/tex] shows motion continues with changing velocity.
### Characteristics of Motion
1. Non-Uniform Acceleration: The body does not move with a constant acceleration throughout. There are intervals with different velocities.
2. Piecewise Linear Segments: The position-time graph has linear segments in various time intervals, indicating varying but constant velocities within those segments.
3. Final Inconsistent Motion (from [tex]\(T = 35\)[/tex] to [tex]\(T = 95\)[/tex]): There is an anomaly in recorded data at [tex]\(T=50\)[/tex], suggesting a data entry error. Otherwise, intervals from [tex]\(T = 35\)[/tex] to [tex]\(T = 95\)[/tex] show erratic motion with small increments in position.
### Conclusion
Upon detailed evaluation, this graph depicts a piecewise linear motion transitioning into a potentially erroneous record at [tex]\(T = 50\)[/tex]. The body initially moves with varying constant speeds before transitioning to a seemingly erratic pattern. Numerically significant intervals show constant speeds of 1 m/s and 2 m/s at different periods.
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline T (s) & 0 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 90 & 95 & 50 \\ \hline X (m) & 5 & 10 & 15 & 25 & 35 & 50 & 60 & 65 & 70 & 73 & 75 \\ \hline \end{array} \][/tex]
### 1. Plotting the Position-Time Graph
To draw the graph, follow these steps:
1. On the x-axis, plot the time (T) in seconds.
2. On the y-axis, plot the position (X) in meters.
3. Mark the coordinates corresponding to each time and position pair.
4. Connect the points to visualize the motion.
### 2. Analysing Motion and its Features
Let's observe the data and the plot we would create:
#### Feature 1: Initial Velocity
- From [tex]\(T = 0\)[/tex] to [tex]\(T = 5\)[/tex]:
[tex]\[ v_1 = \frac{X(5) - X(0)}{T(5) - T(0)} = \frac{10 - 5}{5 - 0} = \frac{5}{5} = 1 \text{ m/s} \][/tex]
#### Feature 2: Consistent Speed Intervals
- From [tex]\(T = 5\)[/tex] to [tex]\(T = 10\)[/tex]:
[tex]\[ v_2 = \frac{X(10) - X(5)}{T(10) - T(5)} = \frac{15 - 10}{10 - 5} = \frac{5}{5} = 1 \text{ m/s} \][/tex]
- From [tex]\(T = 10\)[/tex] to [tex]\(T = 15\)[/tex]:
[tex]\[ v_3 = \frac{X(15) - X(10)}{T(15) - T(10)} = \frac{25 - 15}{15 - 10} = \frac{10}{5} = 2 \text{ m/s} \][/tex]
#### Feature 3: Accelerated Motion
From [tex]\(T = 15\)[/tex] to [tex]\(T = 20\)[/tex], [tex]\(T = 25\)[/tex], etc., the velocity can be observed to change significantly, suggesting acceleration:
- From [tex]\(T = 15\)[/tex] to [tex]\(T = 20\)[/tex]:
[tex]\[ v_4 = \frac{X(20) - X(15)}{T(20) - T(15)} = \frac{35 - 25}{20 - 15} = \frac{10}{5} = 2 \text{ m/s} \][/tex]
- Continued calculation for each segment up to [tex]\(T = 35\)[/tex] shows motion continues with changing velocity.
### Characteristics of Motion
1. Non-Uniform Acceleration: The body does not move with a constant acceleration throughout. There are intervals with different velocities.
2. Piecewise Linear Segments: The position-time graph has linear segments in various time intervals, indicating varying but constant velocities within those segments.
3. Final Inconsistent Motion (from [tex]\(T = 35\)[/tex] to [tex]\(T = 95\)[/tex]): There is an anomaly in recorded data at [tex]\(T=50\)[/tex], suggesting a data entry error. Otherwise, intervals from [tex]\(T = 35\)[/tex] to [tex]\(T = 95\)[/tex] show erratic motion with small increments in position.
### Conclusion
Upon detailed evaluation, this graph depicts a piecewise linear motion transitioning into a potentially erroneous record at [tex]\(T = 50\)[/tex]. The body initially moves with varying constant speeds before transitioning to a seemingly erratic pattern. Numerically significant intervals show constant speeds of 1 m/s and 2 m/s at different periods.
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