What's the kinetic energy of a \(2.4 \times 10^{5}-\mathrm{kg}\) airplane cruising at \(900 \mathrm{km} / \mathrm{h} ?\)

Kinetic energy is the energy that an object possesses due to its motion. To help you understand the kinetic energy equation, imagine it as a quantitative way to express an object's 'energy of motion'. The basic formula to calculate kinetic energy (K.E) is
\[ K.E = \frac{1}{2} mv^2 \]
where \( m \) represents the mass of the object in kilograms (kg) and \( v \) stands for the velocity of the object in meters per second (m/s). In the context of the exercise, calculating the kinetic energy of an airplane in flight involves plugging the airplane's mass and velocity into this formula. Since the equation involves squaring the velocity, even small changes in speed can have a significant impact on the kinetic energy—which highlights why it's critical to get the unit conversion right.

Unit conversion is an essential skill in physics, as it ensures comparisons and calculations are correct and meaningful. When dealing with measurements, converting units to the appropriate standard—like meters per second (m/s) for velocity—allows for correct application of physical formulas. In our exercise, the airplane's speed was given in kilometers per hour (km/h), but the kinetic energy equation requires velocity in meters per second (m/s).
To convert, use the relationships: \(1 \text{ km} = 1000 \text{ m}\) and \(1 \text{ hour} = 3600 \text{ seconds (s)}\). So, the conversion from km/h to m/s is done by multiplying the speed in km/h by \( \frac{1000}{3600} \) or \( \frac{5}{18} \) if simplified. Paying attention to such details is crucial, and practicing unit conversions can dramatically improve the understanding of physical equations and their solutions.

Physical quantities in physics are the measurable attributes of the physical universe, such as mass, length, time, and temperature. These quantities are incredibly important in physics as they are used to quantify the phenomena of the physical world. There are fundamental units like kilograms for mass, meters for length, and seconds for time. However, derived units are also essential, like meters per second for velocity or joules for energy.
In our example, while kinetic energy's SI unit is the joule (J), it is derived from other fundamental units, including kg for mass and m/s for velocity. The joule is itself a compound unit, equivalent to a kilogram meter squared per second squared (kg·m²/s²).
Understanding these physical quantities and their interrelationships is crucial in problem-solving. For instance, it connects mass and velocity with their respective units to yield energy, expressed in joules. Remembering these connections can aid in better comprehension and application of physics principles in various scenarios.