91Ó°ÊÓ

Potential energy is the energy stored in an object due to its position or state. In our exercise, since the person is standing on level ground, we focus on potential energy related to height and gravity. However, because they are not elevated, the potential energy from gravitational height is zero.

Potential energy can come from various sources, such as:

• Gravitational potential energy – determined by height and weight.
• Elastic potential energy – found in stretched or compressed springs.
• Chemical potential energy – stored within chemical bonds.

Since the exercise focuses on someone standing on level ground, there is no height to contribute to gravitational potential energy. Thus, any increase in energy due to running must originate from kinetic energy derived from velocity.

Velocity describes how fast an object is moving in a particular direction. In physics, it is a vector quantity, which means it has both magnitude and direction. For our exercise, the person is initially at rest with a velocity of zero.

As the person begins to run, their velocity changes, which directly affects their kinetic energy. The relationship between velocity and kinetic energy is given by:

• Formula: \( KE = \frac{1}{2} mv^2 \)
• \( m \) represents mass, while \( v \) is velocity.

To double or increase kinetic energy, the velocity must change. Doubling the energy means, theoretically, involving modifications to velocity. Yet, if initial kinetic energy is zero, the notion of doubling initiates from non-zero minimal starting points to assure practical calculations. Thus, velocity changes directly influence total energy calculations.

Total energy is the sum of potential energy and kinetic energy. For this setup, as the person is on level ground and at rest initially, total energy consists predominantly of kinetic energy once motion begins.

In this exercise, we explore changes to total energy through adjustments in kinetic energy, because potential energy remains constant at zero. The goal is to either:

• Double the total energy, which theoretically remains unaltered from zero.
• Increase the total energy by a factor of 10, achieved by raising kinetic energy through increased velocity.

When examining the factor increase, velocity plays a vital role due to its squared relation in kinetic energy. Thus, solving for new velocities involves calculations based on assumed non-zero beginnings, navigating from negligible starting points to accurately quantify energy increments. The exercise calculations involve aligning with real-world scenarios to ensure solutions reflect meaningful increases in total energy.