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What is the magnitude of the net force needed to achieve this motion?

To determine the magnitude of the net force needed to achieve the motion shown in the velocity-time graph, we need to go through the following steps:

### 1. Identify the motion details:
- The graph shows velocity \( v \) (in m/s) plotted against time \( t \) (in seconds). The relationship between velocity and time is linear, indicating uniform acceleration.

- The slope of the line represents the acceleration \( a \), as:
  \[
  a = \frac{\Delta v}{\Delta t}
  \]

  From the graph:
  - Initial velocity \( v_0 = 0 \, \text{m/s} \) at \( t = 0 \, \text{s} \)
  - Final velocity \( v_f = 0.3 \, \text{m/s} \) at \( t = 0.3 \, \text{s} \)

  So, acceleration \( a \) is:
  \[
  a = \frac{0.3 \, \text{m/s}}{0.3 \, \text{s}} = 1 \, \text{m/s}^2
  \]

### 2. Use Newton's Second Law:
To calculate the force, we need the mass \( m \) of the object. Newton's second law states:
\[
F = m \cdot a
\]

- If the mass \( m \) is known, we can compute the net force required to achieve the motion.

### Conclusion:
The acceleration of the object is \( 1 \, \text{m/s}^2 \). To find the net force, you need to know the mass \( m \). If you provide the mass, I can complete the calculation.

Would you like to provide the mass, or should I assume a value for illustrative purposes?

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Here are five questions related to this concept:
1. What is the significance of the slope in a velocity-time graph?
2. How does uniform acceleration differ from non-uniform acceleration?
3. What happens to the net force if the mass of the object is doubled?
4. How is Newton's second law applied to real-world problems like this?
5. Can you describe the relationship between velocity, acceleration, and force?

**Tip:** In physics, the area under a velocity-time graph gives the displacement of the object over that period.

Learn how to determine the magnitude of net force using a velocity-time graph. This problem involves linear motion and Newton's Second Law. Suitable for high school students in Grades 9-12.

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