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The image shows a physics problem related to the motion of a body with a mass of 2 kg. The problem asks for the following:

1. **Equation of motion**: The motion of the body is given by \( x = 7 \cdot t + 4 \cdot t^2 \), where \( x \) is the position in meters and \( t \) is the time in seconds.
  
2. **Required calculations**:
   - **Сила тяжести (Force of gravity)**: \( \text{Н} = \text{mass} \times \text{gravitational acceleration} \)
   - **Начальный импульс тела (Initial momentum of the body)**: \( \text{kg} \cdot \frac{\text{m}}{\text{s}} \)
   - **Начальная кинетическая энергия (Initial kinetic energy)**: \( \text{Дж} \)
   - **Равнодействующая сила (Resultant force)**: \( \text{Н} \)

### Let's solve each part:

1. **Force of gravity**:
   \[
   F_{\text{gravity}} = m \times g = 2 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 19.6 \, \text{N}
   \]

2. **Initial momentum** (at \( t = 0 \)):
   - Velocity \( v(t) \) is found by differentiating \( x(t) \) with respect to time:
     \[
     v(t) = \frac{dx}{dt} = 7 + 8t
     \]
   - At \( t = 0 \), \( v(0) = 7 \, \text{m/s} \).
   - Momentum \( p(0) = m \times v(0) = 2 \, \text{kg} \times 7 \, \text{m/s} = 14 \, \text{kg} \cdot \text{m/s}
   \]

3. **Initial kinetic energy**:
   \[
   E_k(0) = \frac{1}{2} m v(0)^2 = \frac{1}{2} \times 2 \, \text{kg} \times (7 \, \text{m/s})^2 = 49 \, \text{J}
   \]

4. **Resultant force** (determined by the acceleration):
   - Acceleration \( a(t) \) is the derivative of velocity:
     \[
     a(t) = \frac{dv}{dt} = 8 \, \text{m/s}^2
     \]
   - Force \( F_{\text{resultant}} = m \times a = 2 \, \text{kg} \times 8 \, \text{m/s}^2 = 16 \, \text{N}
   \]

### Summary of Results:
- Force of gravity: \( 19.6 \, \text{N} \)
- Initial momentum: \( 14 \, \text{kg} \cdot \text{m/s} \)
- Initial kinetic energy: \( 49 \, \text{J} \)
- Resultant force: \( 16 \, \text{N} \)

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

Here are five related questions you might consider:
1. How would the force of gravity change if the mass was doubled?
2. What would be the initial momentum if the velocity was time-dependent in a more complex way?
3. How does kinetic energy vary if the initial speed is tripled?
4. What is the significance of the resultant force in the context of motion?
5. How can we derive the equation of motion from known forces?

**Tip:** Remember, kinetic energy is proportional to the square of the velocity, meaning that even a small increase in velocity results in a significant increase in energy.

Уравнение движения тела массой 2 кг имеет вид: x = 7 ⋅ t + 4 ⋅ t^2. Вычислите силу тяжести, начальный импульс тела, начальную кинетическую энергию и равнодействующую силу.

Solve a physics problem involving the motion of a 2 kg body. Learn how to calculate the force of gravity, initial momentum, kinetic energy, and resultant force. This problem involves classical mechanics concepts suitable for students in Grades 9-12.

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