Math Problem Statement

The image contains a physics problem related to the motion of a body with a mass of 2 kg. The given equation is: x = 7 + 4t + t^2. The problem involves calculating the total path covered, initial velocity, acceleration, kinetic energy, and applied force.

Solution

The image contains a physics problem related to the motion of a body with a mass of 2 kg. The given equation is:

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

The questions appear to involve calculating the following:

  1. Total path covered (Сумма траекторий): The distance traveled by the body.
  2. Initial velocity (Начальная скорость тела): The initial speed of the body.
  3. Acceleration (Ускорение): The constant acceleration of the body.
  4. Kinetic Energy (Кинетическая энергия): The kinetic energy of the body.
  5. Applied Force (Приложенная сила): The force applied to the body.

Let's calculate each of these:

  1. Initial velocity (v₀):
    The general equation of motion for position x(t)x(t) is given by: x(t)=x0+v0t+12at2x(t) = x_0 + v_0 t + \frac{1}{2} a t^2 Comparing with the given equation x=7+4t+t2x = 7 + 4t + t^2, we find:

    • x0=7x_0 = 7 (initial position)
    • v0=4v_0 = 4 m/s (initial velocity)
    • a=2a = 2 m/s² (acceleration)
  2. Total path covered (distance):
    Since the problem is related to the body's motion with constant acceleration, we should know the time duration to compute the path length.

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Math Problem Analysis

Mathematical Concepts

Kinematics
Quadratic Equations

Formulas

Equation of motion: x(t) = x_0 + v_0 t + (1/2) a t^2
Kinetic energy: K.E. = (1/2) mv^2
Newton's second law: F = ma

Theorems

Newton's Laws of Motion

Suitable Grade Level

Grades 10-12