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Kinetic energy is the energy an object possesses due to its motion. For instance, when a skateboarder moves, they possess kinetic energy, which can be calculated using the formula: \( KE = \frac{1}{2} mv^2 \). Here, \( m \) is the mass, and \( v \) is the velocity of the object.
In practical scenarios like this exercise, knowing the skateboarder's speed helps in determining how much kinetic energy they have both at the beginning and the end of their motion.

• The initial kinetic energy \( (KE_0) \) of the skateboarder was calculated with their starting speed.
• By determining the final speed, we find the final kinetic energy \( (KE_f) \).

The change in kinetic energy is pivotal in analyzing how energy has been transferred or transformed during motion. Such changes give insight into the overall dynamics and help us solve real-world problems involving motion.

Potential energy often relates to the height of an object relative to a specific point, usually the ground. In this context, gravitational potential energy is crucial. It is calculated using the formula: \( PE = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity (approx. \( 9.81 \, \text{m/s}^2 \)), and \( h \) is the height.
This exercise demonstrated a change in the skateboarder's potential energy as they moved vertically.

• The potential energy change \( (\Delta PE) \) reflects how the skateboarder's height has altered.
• A negative change indicates that the skateboarder's vertical position is lower.

Analyzing how potential energy changes can help us understand the vertical movement or height change in various scenarios, such as when an object rises or falls. Understanding these principles is key to problem-solving in physics.

Non-conservative forces are forces where the work done depends on the path taken and not just the initial and final states. Common examples include friction and air resistance. These forces can remove energy from the system or transfer it into other forms, like thermal energy.
In the context of this exercise, two non-conservative forces are at play:

• The skateboarder exerted force by pushing against the ground, adding energy to the system.
• Friction did work on the skateboarder, reducing the system's energy.

The net result of these non-conservative forces significantly impacts the calculations of kinetic and potential energy changes. In this particular scenario, understanding how these forces affect energy helps in pinning down why the skateboarder's height decreases rather than increases after the motion.