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The image provides a problem about the motion of a body with a mass of 2 kg. The equation of motion is given as:

\[
x = 7 \cdot t + 4 \cdot t^2
\]

Let's go step-by-step to solve the following:

1. **Сила тяжести (Gravitational force):**  
   The gravitational force (weight) is calculated as:
   \[
   F_g = m \cdot g
   \]
   where \( m = 2 \, \text{kg} \) and \( g = 9.8 \, \text{m/s}^2 \).  
   
   \[
   F_g = 2 \cdot 9.8 = 19.6 \, \text{N}
   \]

2. **Начальный импульс тела (Initial momentum of the body):**  
   Momentum \( p \) is given by:
   \[
   p = m \cdot v
   \]
   The initial velocity is found by differentiating the position equation \( x(t) \).  
   \[
   v(t) = \frac{dx}{dt} = 7 + 8t
   \]
   At \( t = 0 \), the initial velocity \( v(0) = 7 \, \text{m/s} \). Therefore, the initial momentum is:
   \[
   p = 2 \cdot 7 = 14 \, \text{kg} \cdot \text{m/s}
   \]

3. **Начальная кинетическая энергия (Initial kinetic energy):**  
   Kinetic energy \( K \) is calculated as:
   \[
   K = \frac{1}{2} m v^2
   \]
   At \( t = 0 \), with \( v = 7 \, \text{m/s} \):
   \[
   K = \frac{1}{2} \cdot 2 \cdot 7^2 = \frac{1}{2} \cdot 2 \cdot 49 = 49 \, \text{J}
   \]

4. **Равнодействующая сила (Net force):**  
   The net force is found using Newton's second law \( F = m \cdot a \). The acceleration \( a(t) \) is the derivative of velocity:
   \[
   a(t) = \frac{dv}{dt} = 8 \, \text{m/s}^2
   \]
   Thus, the net force is:
   \[
   F = 2 \cdot 8 = 16 \, \text{N}
   \]

### Summary:

1. **Gravitational Force (H):** \(19.6 \, \text{N}\)
2. **Initial Momentum (kg·m/s):** \(14 \, \text{kg} \cdot \text{m/s}\)
3. **Initial Kinetic Energy (J):** \(49 \, \text{J}\)
4. **Net Force (H):** \(16 \, \text{N}\)

Would you like more details on any of these calculations or have any questions?  

### Related Questions:
1. How would the gravitational force change if the mass was different?
2. What is the significance of kinetic energy in this context?
3. How does the net force affect the motion of the body?
4. How would you calculate the work done by the net force over a given displacement?
5. What would be the body's velocity after 3 seconds? 

### Tip:  
To find velocity or acceleration from position equations, differentiate the position function with respect to time!

Given the motion equation for a body with mass 2 kg as x = 7t + 4t^2, calculate the following: Gravitational Force (N), Initial Momentum (kg·m/s), Initial Kinetic Energy (J), and Net Force (N).

Explore the detailed calculations for a 2 kg body's motion described by x = 7t + 4t^2. Learn how to compute gravitational force, initial momentum, kinetic energy, and net force. Suitable for Grades 11-12 students studying classical mechanics.

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