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.

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.