What is an integral?
An integral is basically a backward derivative. A derivative describes a rate of change. Or, mathematically, the slope of a line (the change in x and y of the coordinates). When you reverse the operation of the derivative, you can determine a sum of all the values in that progression. If you take the integral of a line, you can find the area under the line.
How do you solve for x in a simple algebraic equation? (ie. 2x+8=18)
Put simply, you want to get x by itself on one side. To do that, you have to separate it from all the other numbers (or variables) piece by piece. To follow mathematical rules, you can think of using PEMDAS (parentheses, exponents, multiplication, division, addition subtraction) backward. Start by eliminating all the addition and subtraction, in this case, subtract 8 from both sides. Now the equation is 2x=10. Now, move on do multiplication and division. Divide both sides by 2. x=5. Solved! (In this simple equation, there are no parentheses or exponents).
How are distance, velocity, and acceleration related?
These are all measures of changes. Distance is a change in position. Velocity describes a change in the amount of distance covered in a given time. Acceleration describes the change in velocity at a given time. These three characteristics can create a fairly comprehensive idea of how an object is moving.