The first equation is the integral of torque to velocity, where the torque refers to the force exerted by an external source of energy upon a system and the velocity refers to the velocity of the system. This is also referred to as the Hamilton force law and is often referred to as the force law for a fluid or a solid.

The second equation is the velocity-kinetic energy formula, which expresses the difference of kinetic energy, the amount of energy that is required to make up the kinetic energy of a system, to its potential energy, the amount of energy which can be transformed from kinetic energy to potential energy. The equation for this is known as the conservation law of energy.

The third equation is known as the Lagrange equations, which are more complex than the differential equations. This equation is related to the differential equations in that it involves a differential function. This function is given by an exponential function of time, which can be used to calculate the change of velocity as a function of time.

The fourth equation is called the power law, which is used to calculate the energy of motion. This can be used in applications such as determining the mass-energy balance which results from the relationship between a stationary system and its kinetic energy.

Fourthly, there is the equations for motion according to gravity. These are also known as the equation of position and are used in many applications of physics.

The fifth equation is the displacement-time law, which is used to calculate the change in position of an object in time. This equation is sometimes known as the displacement-time law and can be used in applications such as calculating the position of an object and its acceleration in free-falling objects.

Kinematic equations are necessary for any physical system. Kinematic equations help us determine the motion of a system, especially its acceleration or its change in velocity. They also provide us with the information we need to determine the motion of an object in space or its position and acceleration at various speeds.