# Mathematical Equations in Physics

Physics is a science that depends on mathematics for its calculations. Two of the most important calculations are velocity and acceleration.  If s=displacement, t=time, and v=velocity, then ds/dt=velocity and dv/dt=acceleration.  Velocity is the derivative of displacement with respect to time. Acceleration is the derivative of velocity with respect to time.  Physics uses mathematics to change its calculations to the desired form. Calculus is one of the most important branches of mathematics to physics.

Vectors are used to describe the magnitude and direction of an object in space. Vectors can be added and subtracted.  Vectors can be described on a coordinate plane. They can be two or three dimensions. Vectors can be expressed with a V with an arrow on the top. Scalars are measurements of the magnitude of an object. The equation E=MC^2 is one of the most famous in physics.  It was discovered by Albert Einstein. The E stands for energy, the M for the mass of the object, and C for the speed oflight (3.0×10^8 meters per second). Another important formula is Isaac Newton’s Second Law of Motion: F=MA, where F is the force, M is the mass, and A is the acceleration. Also the formula for work is W=FD, where W is the work, F is the force, and D is the distance.

Also important is the fact the Gravity is always offset by the Normal Force. Gravity is always in a negative direction because the earth drags all objects to it using gravity. The Normal Force is always a vertical force at a right angle to the object. Anotherformula is W=MG, where W is the weight, M is the mass, and G is the acceleration due togravity. The formula for potential energy is P=MGH, where P is the potential energy,M is the mass, G is the acceleration due to gravity, and H is the height of the object fromthe ground. Power is the energy divided by the time, or Power=E/T. Energy can be expressed in joules, weight in newtons, and height in meters. Galileo’s law of falling objects states that all bodies fall at the same rate in a vacuum regardless of the difference in weight. One important part of that statement is the word “vacuum”.

Several branches of mathematics are used in some branches of physics. Calculus is used in classical mechanics. Isaac Newton

discovered calculus at the same time Leibniz did some work on calculus type problems. Newton also compiled the three

laws of motion, a physics concept. Vector calculus is used in electromagnetism. Differential geometry is used in Albert Einstein’s theory of relativity. Matrices and group theory are used in quantum field theory. The mathematical concept

knot theory is used in the physics concept superstring theory.