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Sagot :
Let's analyze the given data step-by-step to determine whether the motion of objects [tex]\(P\)[/tex] and [tex]\(Q\)[/tex] is uniform or non-uniform.
The table provides distances traveled by objects [tex]\(P\)[/tex] and [tex]\(Q\)[/tex] at various times. Here is the data extracted from the table:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Time} & \text{Distance traveled by } P \text{ (meters)} & \text{Distance traveled by } Q \text{ (meters)} \\ \hline 2:00 \, \text{am} & 10 & 12 \\ \hline 5:00 \, \text{am} & 20 & 10 \\ \hline 10:00 \, \text{am} & 30 & 23 \\ \hline 12:15 \, \text{pm} & 40 & 35 \\ \hline 10:19 \, \text{pm} & 80 & 37 \\ \hline 10:50 \, \text{pm} & 60 & 41 \\ \hline 11:00 \, \text{pm} & 70 & 44 \\ \hline \end{array} \][/tex]
### For Object P:
1. Compute the differences in distance traveled between consecutive time points:
- From 2:00 am to 5:00 am: [tex]\(20 - 10 = 10\)[/tex] meters
- From 5:00 am to 10:00 am: [tex]\(30 - 20 = 10\)[/tex] meters
- From 10:00 am to 12:15 pm: [tex]\(40 - 30 = 10\)[/tex] meters
- From 12:15 pm to 10:19 pm: [tex]\(80 - 40 = 40\)[/tex] meters
- From 10:19 pm to 10:50 pm: [tex]\(60 - 80 = -20\)[/tex] meters
- From 10:50 pm to 11:00 pm: [tex]\(70 - 60 = 10\)[/tex] meters
Differences: [tex]\([10, 10, 10, 40, -20, 10]\)[/tex]
2. Check for uniform motion by determining if all differences are equal:
- The differences in distances are not all equal.
Therefore, the motion of object [tex]\(P\)[/tex] is non-uniform.
### For Object Q:
1. Compute the differences in distance traveled between consecutive time points:
- From 2:00 am to 5:00 am: [tex]\(10 - 12 = -2\)[/tex] meters
- From 5:00 am to 10:00 am: [tex]\(23 - 10 = 13\)[/tex] meters
- From 10:00 am to 12:15 pm: [tex]\(35 - 23 = 12\)[/tex] meters
- From 12:15 pm to 10:19 pm: [tex]\(37 - 35 = 2\)[/tex] meters
- From 10:19 pm to 10:50 pm: [tex]\(41 - 37 = 4\)[/tex] meters
- From 10:50 pm to 11:00 pm: [tex]\(44 - 41 = 3\)[/tex] meters
Differences: [tex]\([-2, 13, 12, 2, 4, 3]\)[/tex]
2. Check for uniform motion by determining if all differences are equal:
- The differences in distances are not all equal.
Therefore, the motion of object [tex]\(Q\)[/tex] is non-uniform.
### Conclusion
After analyzing the distance differences:
- The differences for object [tex]\(P\)[/tex] are [tex]\([10, 10, 10, 40, -20, 10]\)[/tex], indicating non-uniform motion.
- The differences for object [tex]\(Q\)[/tex] are [tex]\([-2, 13, 12, 2, 4, 3]\)[/tex], indicating non-uniform motion.
Thus, both objects [tex]\(P\)[/tex] and [tex]\(Q\)[/tex] exhibit non-uniform motion.
The table provides distances traveled by objects [tex]\(P\)[/tex] and [tex]\(Q\)[/tex] at various times. Here is the data extracted from the table:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Time} & \text{Distance traveled by } P \text{ (meters)} & \text{Distance traveled by } Q \text{ (meters)} \\ \hline 2:00 \, \text{am} & 10 & 12 \\ \hline 5:00 \, \text{am} & 20 & 10 \\ \hline 10:00 \, \text{am} & 30 & 23 \\ \hline 12:15 \, \text{pm} & 40 & 35 \\ \hline 10:19 \, \text{pm} & 80 & 37 \\ \hline 10:50 \, \text{pm} & 60 & 41 \\ \hline 11:00 \, \text{pm} & 70 & 44 \\ \hline \end{array} \][/tex]
### For Object P:
1. Compute the differences in distance traveled between consecutive time points:
- From 2:00 am to 5:00 am: [tex]\(20 - 10 = 10\)[/tex] meters
- From 5:00 am to 10:00 am: [tex]\(30 - 20 = 10\)[/tex] meters
- From 10:00 am to 12:15 pm: [tex]\(40 - 30 = 10\)[/tex] meters
- From 12:15 pm to 10:19 pm: [tex]\(80 - 40 = 40\)[/tex] meters
- From 10:19 pm to 10:50 pm: [tex]\(60 - 80 = -20\)[/tex] meters
- From 10:50 pm to 11:00 pm: [tex]\(70 - 60 = 10\)[/tex] meters
Differences: [tex]\([10, 10, 10, 40, -20, 10]\)[/tex]
2. Check for uniform motion by determining if all differences are equal:
- The differences in distances are not all equal.
Therefore, the motion of object [tex]\(P\)[/tex] is non-uniform.
### For Object Q:
1. Compute the differences in distance traveled between consecutive time points:
- From 2:00 am to 5:00 am: [tex]\(10 - 12 = -2\)[/tex] meters
- From 5:00 am to 10:00 am: [tex]\(23 - 10 = 13\)[/tex] meters
- From 10:00 am to 12:15 pm: [tex]\(35 - 23 = 12\)[/tex] meters
- From 12:15 pm to 10:19 pm: [tex]\(37 - 35 = 2\)[/tex] meters
- From 10:19 pm to 10:50 pm: [tex]\(41 - 37 = 4\)[/tex] meters
- From 10:50 pm to 11:00 pm: [tex]\(44 - 41 = 3\)[/tex] meters
Differences: [tex]\([-2, 13, 12, 2, 4, 3]\)[/tex]
2. Check for uniform motion by determining if all differences are equal:
- The differences in distances are not all equal.
Therefore, the motion of object [tex]\(Q\)[/tex] is non-uniform.
### Conclusion
After analyzing the distance differences:
- The differences for object [tex]\(P\)[/tex] are [tex]\([10, 10, 10, 40, -20, 10]\)[/tex], indicating non-uniform motion.
- The differences for object [tex]\(Q\)[/tex] are [tex]\([-2, 13, 12, 2, 4, 3]\)[/tex], indicating non-uniform motion.
Thus, both objects [tex]\(P\)[/tex] and [tex]\(Q\)[/tex] exhibit non-uniform motion.
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