https://file.aiquickdraw.com/mathbot/file/1728036231225gfj0kqdl.jpg

Let's break down the questions in the diagram.

### Part (a) - **Uniform Speed**
The velocity-time graph shows a section where the speed is constant (uniform). From the graph, this happens between 20 seconds and 30 seconds, where the speed is **15 m/s**.

### Part (b) - **Distance Travelled in the First 20 Seconds**
The total distance traveled can be found by calculating the area under the velocity-time graph. The first 20 seconds consists of:
1. **0 to 15 seconds**: This forms a trapezium.
   - Heights: 0 m/s to 40 m/s.
   - Base (time): 15 seconds.
   
   Area of trapezium = \(\frac{1}{2} \times (40 + 15) \times 15 = 412.5 \text{ m}\).

2. **15 to 20 seconds**: This is a rectangle.
   - Speed: 15 m/s.
   - Time: 5 seconds.

   Area of rectangle = \(15 \times 5 = 75 \text{ m}\).

**Total distance in first 20 seconds = 412.5 m + 75 m = 487.5 m**.

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### Answers:
**(a)**: 15 m/s.  
**(b)**: 487.5 m.

Would you like more details or have any questions on this?

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Here are 5 follow-up questions:
1. What is the significance of the area under a velocity-time graph?
2. How do you calculate the distance for a non-uniform velocity?
3. How do you find the total distance when the graph is complex?
4. How would the graph change if the acceleration was negative throughout?
5. Can you explain the physical meaning of the slope in the first 15 seconds?

**Tip**: Always check if the graph's sections form simple shapes (like triangles or rectangles) to make area calculations easier.

Diagram 4 shows the velocity-time graph of a particle over a period of 30 seconds. (a) State the uniform speed, in ms^-1, of the particle. (b) Calculate the distance travelled by this particle in the first 20 seconds.

Learn how to find the uniform speed and calculate the distance travelled by a particle using a velocity-time graph. The problem demonstrates key concepts in kinematics, such as reading graphs and applying area formulas. Suitable for students in Grades 9-11.

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