Math Problem Statement

The image shows a physics problem where the equation of motion for a body with a mass of 2 kg is given as: x = 7 * t + 4 * t^2. You are required to find the Gravitational Force (N), Initial Momentum (kg·m/s), Initial Kinetic Energy (J), and Resultant Force (N).

Solution

The image shows a physics problem where the equation of motion for a body with a mass of 2 kg is given as:

x=7t+4t2x = 7 \cdot t + 4 \cdot t^2

You are required to find:

  1. Gravitational Force (N): This is the weight of the object.
  2. Initial Momentum (kg·m/s): The momentum at t=0t = 0.
  3. Initial Kinetic Energy (J): The kinetic energy at t=0t = 0.
  4. Resultant Force (N): The net force acting on the body.

Let's break down each step:

  1. Gravitational Force (N): Fg=mgF_g = m \cdot g Where m=2kgm = 2 \, \text{kg} and g9.8m/s2g \approx 9.8 \, \text{m/s}^2. Fg=2×9.8=19.6NF_g = 2 \times 9.8 = 19.6 \, \text{N}

  2. Initial Momentum (kg·m/s): Momentum pp is given by p=mvp = m \cdot v, where ( v

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Math Problem Analysis

Mathematical Concepts

Kinematics
Newton's Second Law
Momentum
Kinetic Energy

Formulas

F_g = m * g
p = m * v
K = 1/2 * m * v^2
F = m * a

Theorems

Newton's Second Law
Equation of Motion

Suitable Grade Level

Grades 10-12