"Today we worked on many topics, the largest of which was particle motion.
These problems can go one of three different ways. Sometimes, you are provided with an equation for position, and you have to take derivatives of it to get the equation for velocity and then take the derivative of the velocity to find the equation for acceleration.
Another question topic in particle motion is when you are given an equation for acceleration, and then integrate it in order to find the equation for velocity. When you do this, you end up with a constant +C which you then need to find using a constraint. A constraint tells you the value of the function given a specific input. The question will say something like: "the velocity at t = 10s is 40 m/s" Once you plug in this point, you get a numerical value for C. Then you can re-write your velocity equation and then integrate that in order to find the equation for particle motion +C. You then need to solve for that =C using a different initial condition, this time for position.
The final question type in particle motion is if you are asked to find the total displacement VS total distance traveled. To find displacement, simply find the integral of the velocity function. If you are asked to find the total distance traveled, then you should find the integral of the absolute value of the velocity function.
To do this, the first step is to find for which values of t your velocity function is positive and which values of t yield negative value for velocity. Do this by setting your velocity equation equal to 0 and solving for t. Then graph your end points, and each zero point on a number line and determine whether your function is positive or negative in between each of these points which you have marked on your number line. Then, you need to evaluate the integral of the velocity for each sub-section interval which you've just created. The trick is to negate the terms which are going to give you a negative distance, to make it a positive distance. In this way, instead of getting the displacement, you get the total distance traveled.
This brought us to the end of the session."