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The question provides a force-time graph for a body with a mass of \(8 \, \text{kg}\) and asks for the change in velocity of the body. To solve this, we will use the following key concepts:

1. **Impulse-Momentum Theorem:**  
   Impulse (\( J \)) is the area under the force-time graph, and it is related to the change in momentum (\( \Delta p \)) of the body by:
   \[
   J = \Delta p = m \Delta v
   \]
   where:
   - \( J \) is the impulse,
   - \( m \) is the mass of the body, and
   - \( \Delta v \) is the change in velocity.

2. **Steps:**
   - First, calculate the area under the force-time graph to find the impulse.
   - Then, use the relationship between impulse and change in momentum to find the change in velocity.

### Breakdown of the graph:
- From \( t = 0 \) to \( t = 10 \, \text{s} \), the force increases linearly from \( 0 \, \text{N} \) to \( 10 \, \text{N} \).
- From \( t = 10 \, \text{s} \) to \( t = 20 \, \text{s} \), the force is constant at \( -2 \, \text{N} \).

Now, let's calculate the area under each section:

1. **From \( t = 0 \, \text{s} \) to \( t = 10 \, \text{s} \) (a triangle):**
   - The area is given by:
     \[
     \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 10 \, \text{s} \times 10 \, \text{N} = 50 \, \text{Ns}
     \]

2. **From \( t = 10 \, \text{s} \) to \( t = 20 \, \text{s} \) (a rectangle):**
   - The area is given by:
     \[
     \text{Area} = \text{Base} \times \text{Height} = 10 \, \text{s} \times (-2) \, \text{N} = -20 \, \text{Ns}
     \]

### Total Impulse:
\[
J = 50 \, \text{Ns} + (-20) \, \text{Ns} = 30 \, \text{Ns}
\]

### Change in velocity:
Using the impulse-momentum theorem:
\[
J = m \Delta v
\]
\[
30 \, \text{Ns} = 8 \, \text{kg} \times \Delta v
\]
\[
\Delta v = \frac{30}{8} = 3.75 \, \text{m/s}
\]

Thus, the change in velocity of the body is **3.75 m/s**.

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Would you like further details or have any other questions?

Here are five related questions for further practice:
1. What would be the change in velocity if the mass of the body were 10 kg instead of 8 kg?
2. How would the result change if the force-time graph had a negative slope after 10 seconds?
3. How do you calculate impulse from a force that varies non-linearly with time?
4. How is the impulse-momentum theorem related to Newton's second law of motion?
5. What happens to the change in velocity if the area under the graph were zero?

**Tip:** In force-time problems, always focus on calculating the area under the graph to determine the impulse applied to the object.

The force-time graph for the motion of a body of mass 8 kg moving along a straight line is shown in the figure. Find the change in velocity of the body in SI units.

This problem involves calculating the change in velocity of a body with a mass of 8 kg using a force-time graph. Learn how to apply the Impulse-Momentum Theorem and determine the total impulse from the graph. Suitable for high school students studying physics in grades 10-12.

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