Calculating Kinetic Energy of an Object

This question asks us to determine the kinetic energy of an object given its mass and velocity. Kinetic energy is the energy an object possesses due to its motion. To solve this, we need to use the formula for kinetic energy.

Understanding Kinetic Energy

Kinetic energy depends on two factors: the mass of the object and its speed (or velocity). The faster an object moves and the more massive it is, the more kinetic energy it has.

Formula for Kinetic Energy

The formula used to calculate kinetic energy (KE) is:

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

Where:

• \(m\) is the mass of the object
• \(v\) is the velocity (speed) of the object
• KE is the kinetic energy, typically measured in Joules (J)

Applying the Formula to the Problem

We are given the following information:

• Mass (\(m\)) = 22 kg
• Velocity (\(v\)) = 5 m/s

Now, we substitute these values into the kinetic energy formula:

$$KE = \frac{1}{2} \times 22 \, \text{kg} \times (5 \, \text{m/s})^2$$

First, calculate the square of the velocity:

$$(5 \, \text{m/s})^2 = 5 \times 5 \, (\text{m/s})^2 = 25 \, \text{m}^2/\text{s}^2$$

Now substitute this back into the formula:

$$KE = \frac{1}{2} \times 22 \, \text{kg} \times 25 \, \text{m}^2/\text{s}^2$$

Multiply the values:

$$KE = 11 \times 25 \, \text{kg} \cdot \text{m}^2/\text{s}^2$$

$$KE = 275 \, \text{kg} \cdot \text{m}^2/\text{s}^2$$

The unit kg⋅m²/s² is equivalent to the Joule (J), the standard unit of energy.

So, the kinetic energy is 275 J.

Verification with Options

Let's compare our calculated value with the given options:

Our calculated kinetic energy of 275 J matches option 1.

Revision Table: Kinetic Energy Concepts

Additional Information on Kinetic Energy and Motion

Understanding kinetic energy is fundamental in physics, particularly in mechanics. Here are some related points:

• Relationship with Work: The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Work done is the transfer of energy.
• Factors Affecting KE: Kinetic energy is directly proportional to the mass (\(m\)) and the square of the velocity (\(v^2\)). This means doubling the mass doubles the kinetic energy, but doubling the velocity quadruples the kinetic energy.
• Types of Kinetic Energy: While \(KE = \frac{1}{2}mv^2\) is for translational kinetic energy (energy due to linear motion), objects can also have rotational kinetic energy (energy due to spinning), which has a different formula.
• Conservation of Energy: In a closed system where only conservative forces (like gravity or elastic force) are doing work, the total mechanical energy (the sum of kinetic and potential energy) remains constant. Kinetic energy can be converted into potential energy and vice versa.

This calculation demonstrates a simple application of the kinetic energy formula, which is a key concept in understanding the mechanics of moving objects.