The image provides the velocity-time graph of an object moving along the x-axis. The object has a mass of $4.1 \, \text{kg}$. You are tasked with finding the x-component of the net force acting on the object at $t = 1 \, \text{s}$.

Steps to Solve:

1. Find acceleration at $t = 1 \, \text{s}$:

   • From the graph, the velocity increases linearly between $t = 0 \, \text{s}$ and $t = 2 \, \text{s}$, indicating constant acceleration during this interval.
   • The velocity at $t = 0 \, \text{s}$ is $0 \, \text{m/s}$, and at $t = 2 \, \text{s}$, it reaches $12 \, \text{m/s}$.

   The acceleration $a_x$ during this time interval can be found using the slope of the velocity-time graph: $a_x = \frac{\Delta v_x}{\Delta t} = \frac{12 \, \text{m/s} - 0 \, \text{m/s}}{2 \, \text{s} - 0 \, \text{s}} = 6 \, \text{m/s}^2$

2. Use Newton's Second Law: Newton’s second law states: $F_{\text{net}, x} = m a_x$ where $m = 4.1 \, \text{kg}$ is the mass of the object, and $a_x = 6 \, \text{m/s}^2$.

   Substituting the values: $F_{\text{net}, x} = 4.1 \, \text{kg} \times 6 \, \text{m/s}^2 = 24.6 \, \text{N}$

Final Answer:

The x-component of the net force acting on the object at $t = 1 \, \text{s}$ is $24.6 \, \text{N}$.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:

1. What would the net force be at $t = 4 \, \text{s}$?
2. How do you calculate force when velocity is decreasing?
3. What happens to the net force when the velocity is constant?
4. How does mass affect the net force when acceleration is known?
5. How would the graph change if the object had a different mass?

Tip: Always check the slope of a velocity-time graph to find the acceleration, as acceleration is directly related to the net force.