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To draw the velocity vs. time graph based on the given position-time graph, we need to analyze the slope of each segment of the graph, as the velocity is the rate of change of position with respect to time.

### Step-by-step breakdown:
1. **From \( t = 0 \) to \( t = 1 \) second:**
   - The graph rises from 1 meter to 2 meters.
   - Slope \( \frac{\Delta s}{\Delta t} = \frac{2 - 1}{1 - 0} = 1 \, \text{m/s} \).
   - So, velocity = \( 1 \, \text{m/s} \).

2. **From \( t = 1 \) to \( t = 2 \) seconds:**
   - The graph remains flat (horizontal line at 2 meters).
   - Slope = 0, meaning the object is not moving.
   - So, velocity = \( 0 \, \text{m/s} \).

3. **From \( t = 2 \) to \( t = 3 \) seconds:**
   - The graph decreases from 2 meters to 1 meter.
   - Slope \( \frac{\Delta s}{\Delta t} = \frac{1 - 2}{3 - 2} = -1 \, \text{m/s} \).
   - So, velocity = \( -1 \, \text{m/s} \).

4. **From \( t = 3 \) to \( t = 5 \) seconds:**
   - The graph remains flat (horizontal line at 1 meter).
   - Slope = 0, meaning the object is stationary again.
   - So, velocity = \( 0 \, \text{m/s} \).

5. **From \( t = 5 \) to \( t = 6 \) seconds:**
   - The graph rises from 1 meter to 5 meters.
   - Slope \( \frac{\Delta s}{\Delta t} = \frac{5 - 1}{6 - 5} = 4 \, \text{m/s} \).
   - So, velocity = \( 4 \, \text{m/s} \).

### Velocity vs. Time Plot:
- From \( t = 0 \) to \( t = 1 \) second: \( v = 1 \, \text{m/s} \).
- From \( t = 1 \) to \( t = 2 \) seconds: \( v = 0 \, \text{m/s} \).
- From \( t = 2 \) to \( t = 3 \) seconds: \( v = -1 \, \text{m/s} \).
- From \( t = 3 \) to \( t = 5 \) seconds: \( v = 0 \, \text{m/s} \).
- From \( t = 5 \) to \( t = 6 \) seconds: \( v = 4 \, \text{m/s} \).

Would you like me to draw the velocity-time graph based on this information?

Learn how to draw the velocity vs. time graph based on a position-time graph. Analyze the slope of each segment and understand the relation between position and velocity. This problem involves key kinematics concepts and is suitable for students in Grades 9-12.

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