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نمودار سرعت-زمان متحرکی  که بر مسیری مستقیم حرکت می کند، به صورت شکل زیر است. مسافت پیموده شده توسط این متحرک در بازه زمانی  0ثانیه تا 20 ثانیه ، چند متر است؟

To solve this problem, we need to calculate the area under the velocity-time graph. The area represents the total displacement or the distance traveled over the given time interval. Let me analyze the graph and break it down step by step.

### Analysis of the Graph:
The graph is divided into geometric shapes—mostly triangles and possibly a trapezoid or triangle near the time \( t = 20 \) seconds. We can compute the areas of these individual shapes to determine the total distance traveled.

1. **Between \( t = 0 \) to \( t = 10 \) seconds**:
   - The graph forms a triangle with a base of \( 10 \, s \) and a height of \( 12 \, m/s \).

2. **Between \( t = 10 \) to \( t = 20 \) seconds**:
   - The graph forms another triangle, but now it slopes downwards, representing a deceleration from \( v = 12 \, m/s \) to \( v = -4 \, m/s \).

#### Steps to Solve:
1. Compute the area of the triangle for \( 0 \leq t \leq 10 \) seconds.
2. Compute the area for \( 10 \leq t \leq 20 \) seconds.
3. Add the absolute values of these areas to find the total distance traveled.

I will now calculate these areas.The total distance traveled by the object over the time interval from 0 to 20 seconds is \( 140 \, \text{meters} \).

Would you like further details on this calculation or have any other questions?

Here are 5 related questions:
1. How do we compute displacement if the object changes direction?
2. What is the difference between distance and displacement in this context?
3. How does the shape of the velocity-time graph affect the object's motion?
4. How can we calculate acceleration from a velocity-time graph?
5. What would the total distance be if the velocity had a more complex variation?

**Tip:** Always use the absolute value of the area under the graph for total distance, regardless of direction changes, as negative areas indicate direction reversal (not reduced distance).

نمودار سرعت-زمان متحرکی  که بر مسیری مستقیم حرکت می کند، به صورت شکل زیر است. مسافت پیموده شده توسط این متحرک در بازه زمانی 0ثانیه تا 20 ثانیه ، چند متر است؟

Learn how to calculate the total distance traveled by an object from a velocity-time graph over a 20-second interval. Using geometric areas under the graph, this kinematics problem demonstrates the relationship between velocity and distance. Suitable for Grades 9-12.

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