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Kinetic energy is a fundamental concept in physics that describes the energy an object possesses due to its motion. It is given by the formula \frac{1}{2}mv^{2}\, where \(m\) represents the mass of the object and \(v\) represents its velocity.

Kinetic energy is measured in joules (J). The formula essentially calculates the work needed to accelerate an object of mass \(m\) from rest to a velocity \(v\).

For example, when you throw a ball, it gains kinetic energy proportional to its mass and the square of its speed. This is why, for instance, a heavier object or one moving faster will have more kinetic energy.

Substitution in formulas is a mathematical process that involves replacing variables in an equation with actual numerical values. This is crucial for evaluating expressions and solving problems.

For the given exercise, the formula for kinetic energy is \frac{1}{2}mv^{2}\. By substituting \(m = 2.5\) (mass in kilograms) and \(v = 6\) (velocity in meters per second), we replace the variables with known values.

This step transforms the general formula into a specific numerical calculation: \frac{1}{2}2.5(6^{2})\. Substitution helps in breaking down complex formulas into simpler arithmetic operations, making it easier to solve the problem.

Remember, substitution is widely used not only in physics but in different branches of math and science, making it a versatile tool for solving various types of equations.

Basic arithmetic operations are the fundamental building blocks of mathematics. They include addition, subtraction, multiplication, and division.

In the given exercise, several arithmetic operations are performed:

• First, we calculated the square of the velocity by squaring 6, resulting in 36: \(6^{2} = 36\).
• Next, we multiplied the mass (2.5) by this result: \(2.5 \times 36 = 90\).
• Finally, we multiplied by \(\frac{1}{2}\) to get the final kinetic energy: \(\frac{1}{2} \times 90 = 45\).

Each of these steps involves simple arithmetic operations. Squaring a number is a form of multiplication, while multiplying by a fraction is a basic application of division.

Understanding and mastering these operations helps in solving more complex mathematical problems efficiently. By breaking down a problem into smaller, manageable steps, students can tackle even challenging calculations with ease.