What is the order of operations?
The acronym is P.E.M.D.A.S. I remember the acronym as "Please Excuse My Dear Aunt Sally." Calculate numbers in parenthesis first, then compute numbers or variables with exponents, then multiply and divide numbers (from left to right in the equation), and then add and subtract numbers (from left to right).
How are position, velocity, and acceleration vs. time graphs of a particle related to each other in terms of derivatives and integrals?
In a position vs. time graph, the slope of the tangent line at a particular point, or the derivative, is the velocity of the particle at that point. The curvature at that point, or the double derivative, is the acceleration of the particle at that point. In a velocity vs. time graph, the slope of the tangent line at a particular point, or the derivative, is the acceleration of the particle at that point. The integral, or the area under the curve, would yield the displacement, or the total distance traveled, or the particle. In an acceleration vs. time graph, the integral would yield the velocity of the particle. Taking the integral twice would yield position.
What are some important rules to remember when using the quadratic formula?
The quadratic formula is used to solve quadratic equations, and these equations usually yield two answers for the variable. Quadratic equations are equations that have a variable (usually x or y) to the second power. Also, the quadratic formula cannot be used if the coefficient of the squared variable equals zero.