https://file.aiquickdraw.com/mathbot/file/1726049092796agukh48q.jpg

Let's analyze the graph and address each part of the question systematically:

### Part (a) - Find the velocity at specific times:

1. **At \( t = 0 \)**: 
   From the graph, the velocity at \( t = 0 \) is around \( 6 \, \text{m/s} \).

2. **At \( t = 1 \)**:
   From the graph, the velocity at \( t = 1 \) is around \( 4 \, \text{m/s} \).

3. **At \( t = 2 \)**:
   From the graph, the velocity at \( t = 2 \) is \( 0 \, \text{m/s} \).

### Part (b) - Describe what is happening in the first 2 seconds:

- From \( t = 0 \) to \( t = 2 \), the velocity of the particle is **decreasing linearly**, going from \( 6 \, \text{m/s} \) at \( t = 0 \) to \( 0 \, \text{m/s} \) at \( t = 2 \). This suggests the particle is **slowing down** during this time.

### Part (c) - When is the particle stationary?

- The particle is stationary when the velocity is \( 0 \, \text{m/s} \). This occurs at:
  - \( t = 2 \) seconds and \( t = 6 \) seconds.

### Part (d) - Describe what happens when \( v = 0 \):

- When the velocity is \( 0 \, \text{m/s} \), the particle is momentarily at rest. This happens at \( t = 2 \) and \( t = 6 \), likely indicating a change in the direction of motion after these points.

### Part (e) - When is the velocity increasing?

- The velocity is increasing:
  - From \( t = 2 \) to \( t = 4 \) (velocity increases from \( 0 \, \text{m/s} \) to \( 6 \, \text{m/s} \)).

### Part (f) - When is the velocity constant?

- The velocity is constant:
  - From \( t = 4 \) to \( t = 5 \) (velocity is \( 6 \, \text{m/s} \)).

### Part (g) - When is the particle moving in a positive direction?

- The particle is moving in the positive direction when the velocity is positive (above the x-axis):
  - From \( t = 0 \) to \( t = 2 \), and from \( t = 2 \) to \( t = 5 \).

### Part (h) - When is the particle moving in a negative direction?

- The particle is moving in the negative direction when the velocity is negative (below the x-axis):
  - From \( t = 5 \) to \( t = 7 \).

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Would you like more detailed explanations or further clarification? Here are five related questions for deeper understanding:

1. How can you calculate the total displacement of the particle over the given time period?
2. What does the slope of the velocity graph represent physically?
3. How can you find the total distance traveled by the particle?
4. How does the acceleration change during the different time intervals?
5. Can you determine the particle’s average velocity over the entire time interval?

### Tip: 
Always check whether the velocity graph crosses the time axis to identify when the particle changes direction.

The graph shows the velocity of a particle over time. Questions ask for velocity at specific times, when the particle is stationary, and describe its motion over different time intervals.

Learn how to analyze a velocity-time graph for a particle's motion over time. This problem involves determining velocities at specific times, understanding when the particle is stationary, and describing its motion in different intervals. Suitable for high school students studying physics and kinematics.

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