Math Problem Statement
Solution
This image contains a position-time graph along with related questions in Persian. Here's the breakdown of the questions and an explanation of how to address them based on the graph provided:
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Question (الف):
"مسافت طی شده در ۴ ثانیه اول حرکت چند متر است؟"
Translation:
"What is the distance traveled during the first 4 seconds of motion?"Solution:
- To calculate the total distance, observe the absolute value of the graph in the first 4 seconds. Sum the lengths of all segments regardless of direction.
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Question (ب):
"در چه لحظاتی متحرک تغییر جهت داده است؟"
Translation:
"At which moments does the object change direction?"Solution:
- The object changes direction at points where the slope of the graph changes sign (crosses the x-axis).
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Question (پ):
"در لحظاتی که متحرک در خلاف جهت محور حرکت کرده است مسافت طی شده چند متر بوده است؟"
Translation:
"During the moments when the object moves in the opposite direction of the axis, how much distance is traveled?"Solution:
- Identify the intervals where the graph is below the x-axis (negative position). Calculate the total absolute distance traveled in these intervals.
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Question (ت):
"در چه لحظاتی مکان متحرک تغییر جهت داده است؟"
Translation:
"At which moments does the position of the object change direction?"Solution:
- Similar to question (ب), the moments of change in direction are when the graph crosses the x-axis.
Would you like a detailed step-by-step calculation for each question? Let me know!
Related Questions:
- How do you calculate the total displacement during the first 4 seconds?
- How can you determine the velocity at any given time from the graph?
- What is the difference between displacement and distance in motion graphs?
- Can this type of graph represent acceleration, or is it only for position?
- How do we distinguish between instantaneous velocity and average velocity using such a graph?
Tip:
To solve motion-related problems effectively, always distinguish between scalar (distance) and vector (displacement) quantities.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Graph Analysis
Position-Time Graph
Formulas
Distance = sum of absolute displacements
Direction change occurs when velocity changes sign
Theorems
Displacement vs. Distance
Velocity and direction relationships
Suitable Grade Level
Grades 9-11
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