https://file.aiquickdraw.com/mathbot/file/1727604174726kihj3kk6.pdf

Let's start with **Question 5** from the document:

### **Question 5:**
Learners are investigating the effect of mass on the speed of an object, using the data below:

| **Mass (kg)** | **Velocity (m.s⁻¹)** |
|---------------|----------------------|
| 0.10          | 0.15                 |
| 0.15          | 0.39                 |
| 0.20          | 0.58                 |
| 0.25          | 0.65                 |
| 0.35          | 0.91                 |
| 0.45          | 1.17                 |
| 0.50          | 1.40                 |
| 0.55          | 1.43                 |

**5.1 Identify:**

- **5.1.1** The dependent variable (1 mark)
    - The dependent variable is **velocity** (m.s⁻¹), as it changes based on the mass.

- **5.1.2** The independent variable (1 mark)
    - The independent variable is **mass** (kg), which is controlled or changed during the investigation.

**5.2** Plot a line graph that represents the relationship between mass and speed (6 marks)

- Mass will be on the **x-axis** and velocity on the **y-axis**. I can provide guidance for creating this graph or help plot it if you need.

**5.3** Use the graph to determine the velocity when the mass is 0.30 kg (2 marks)

- From the data trend, when mass increases, velocity also increases. Interpolating between the values, we estimate that at **0.30 kg**, the velocity will be around **0.77 m.s⁻¹**.

**5.4** Use the graph to calculate the momentum of the object (3 marks)

- Momentum (p) = mass (m) × velocity (v)
- If we use the velocity at **0.30 kg**:
    - \( p = 0.30 \, \text{kg} \times 0.77 \, \text{m.s⁻¹} = 0.231 \, \text{kg.m.s⁻¹} \)

Let me know if you'd like any clarifications or further assistance on this.

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Here are **5 related questions** for additional practice:
1. What is the relationship between mass and velocity based on the graph?
2. How does momentum vary with changes in mass at constant velocity?
3. How would increasing the force applied to the object affect the velocity and momentum?
4. If the surface is frictionless, what would happen if the mass doubles?
5. How could the experiment be modified to measure the impact of air resistance on velocity?

**Tip**: When plotting graphs, make sure the axes are labeled correctly, with appropriate scales for easier data interpretation!

Explore the relationship between mass and velocity in this Grade 12 Physics problem. This question examines the effects of mass on the speed of an object and the calculation of momentum. It includes data interpretation and graphing, perfect for students studying linear motion and momentum.

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