Recall the expressions for gravitational potential and kinetic energy of an object

Gravitational Potential Energy: Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. The expression for gravitational potential energy (PE) is given by the equation:

PE = mgh

where m represents the mass of the object, g represents the acceleration due to gravity, and h represents the height or vertical distance of the object from a reference point.

For example, if we consider a ball of mass m that is lifted to a height h above the ground, the gravitational potential energy of the ball is given by the product of its mass, the acceleration due to gravity, and the height it is lifted to.

Kinetic Energy: Kinetic energy is the energy possessed by an object due to its motion. The expression for kinetic energy (KE) is given by the equation:

KE = (1/2)mv^2

where m represents the mass of the object and v represents the velocity of the object.

If we consider the same ball that was lifted to a height and then released, as it falls downward, its potential energy is converted into kinetic energy. The kinetic energy of the ball is given by half the product of its mass and the square of its velocity.

The expression for kinetic energy shows that the kinetic energy of an object is proportional to its mass and the square of its velocity. This means that an object with a larger mass or a higher velocity will possess more kinetic energy.

It's important to note that both gravitational potential energy and kinetic energy are scalar quantities, meaning they have magnitude but no specific direction. They are both measured in units of energy, such as joules (J).

In summary, the expressions for gravitational potential energy and kinetic energy provide insights into the energy possessed by an object. Gravitational potential energy is determined by the mass of the object, the acceleration due to gravity, and its height from a reference point. Kinetic energy, on the other hand, depends on the mass of the object and its velocity. Understanding these expressions helps us analyze and quantify the energy changes associated with the position and motion of objects in various scenarios.