Writings

A difficult AP Physics problem rarely feels difficult because of one equation. More often, a student is trying to hold several ideas at once: what the diagram means, which forces matter, whether velocity and acceleration point the same way, and why a familiar formula does not seem to fit. An online AP Physics tutor helps slow that process down, organize it, and make each step understandable.

AP Physics is demanding because it asks students to reason, not simply recall. A student may memorize Newton’s laws and still freeze when a block is pulled across an incline. They may know the equation for electric potential but not see how it connects to energy. Good support does not replace that reasoning with shortcuts. It teaches the student how to build it.

We all have heard of it. The quadratic formula. It is a very well known formula that allows us to solve any arbitrary quadratic equation by just substituting the values of the coefficients. But where does it come from? How do we know it’s correct? Here we will answer this question.

The problem

We need to find an x that satisfies the equation

for all coefficients a, b and c. The way in which we could do this is simple. What we do first is to multiply both sides by 4a. This way, we get

How long is a degree of latitude? How long is a degree of longitude? These are questions someone may have asked when reading about longitude and latitude. With the help of spherical geometry, these questions can be answered.

Length of a degree of latitude (modeling the Earth as a perfect sphere)

Let’s imagine, on a sphere, a line of longitude. Meaning, a set of points all having the same longitude with varying latitudes. In geography, this is often called a meridian. So we can use the following illustration to make this derivation:
From this, it’s easy to see that the formula for the length of an arc of a circle applies: