Calculating Kinetic Energy

The question asks us to find the kinetic energy of an object given its mass and uniform velocity. Kinetic energy is the energy that an object possesses due to its motion. The formula for calculating kinetic energy is fundamental in physics.

Understanding Kinetic Energy

Kinetic energy depends on two factors: the mass of the object and its velocity. The greater the mass or velocity, the greater the kinetic energy. The relationship is given by the formula:

$$ KE = \frac{1}{2}mv^2 $$

Where:

• \( KE \) is the kinetic energy
• \( m \) is the mass of the object
• \( v \) is the velocity of the object

The standard unit for kinetic energy in the International System of Units (SI) is the Joule (J).

Given Information

From the question, we are given the following values:

• Mass of the object, \( m = 15 \) kg
• Velocity of the object, \( v = 4 \) m/s

Step-by-Step Kinetic Energy Calculation

Now, we can substitute the given values of mass and velocity into the kinetic energy formula:

Step 1: Write down the formula for kinetic energy.

$$ KE = \frac{1}{2}mv^2 $$

Step 2: Substitute the given values for mass (\( m \)) and velocity (\( v \)).

$$ KE = \frac{1}{2} \times 15 \text{ kg} \times (4 \text{ m/s})^2 $$

Step 3: Calculate the square of the velocity.

$$ (4 \text{ m/s})^2 = 4^2 \text{ m}^2/\text{s}^2 = 16 \text{ m}^2/\text{s}^2 $$

Step 4: Substitute the squared velocity back into the formula.

$$ KE = \frac{1}{2} \times 15 \text{ kg} \times 16 \text{ m}^2/\text{s}^2 $$

Step 5: Perform the multiplication.

$$ KE = \frac{1}{2} \times (15 \times 16) \text{ kg} \cdot \text{m}^2/\text{s}^2 $$

$$ KE = \frac{1}{2} \times 240 \text{ kg} \cdot \text{m}^2/\text{s}^2 $$

Step 6: Calculate the final kinetic energy.

$$ KE = 120 \text{ kg} \cdot \text{m}^2/\text{s}^2 $$

The unit kg·m²/s² is equivalent to the Joule (J).

So, the kinetic energy possessed by the object is 120 J.

Result Summary

The calculation shows that an object with a mass of 15 kg moving at a uniform velocity of 4 m/s has a kinetic energy of 120 Joules.

Revision Table: Key Physics Concepts

Additional Information: Energy and Motion

Energy is a fundamental concept in physics. It exists in many forms, including kinetic energy, potential energy, thermal energy, chemical energy, etc. The total energy of an isolated system remains constant; this is known as the law of conservation of energy.

Potential Energy: While kinetic energy is energy of motion, potential energy is stored energy. Gravitational potential energy, for example, is the energy an object possesses due to its position in a gravitational field, given by \( PE = mgh \) (where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is height).

Work and Energy: Work done on an object is related to the change in its energy. The Work-Energy Theorem states that the net work done on an object is equal to the change in its kinetic energy (\( W_{net} = \Delta KE \)).

Uniform Velocity: The question mentions uniform velocity. This means the object is moving at a constant speed in a straight line. While the calculation of kinetic energy only uses the magnitude of velocity (speed), the concept of uniform velocity implies zero acceleration, which is relevant in broader mechanics problems.