★
★
★
★
★

"During today's session, we started with some Spanish review of a worksheet testing the difference between the imperfect and preterite past tenses. The student had a list of rules for each tense to help differentiate them; preterite generally serves to advance a narrative and has either an explicitly labeled date/time of action or, from context, a definite ending point. She did very well in this exercise and was excellent in her understanding of the differences between the two tenses; the one area where she needs a little more review is the conjugation of the verbs themselves, which comes down to making flashcards or just repetition of the regular -ar, -er and -ir imperfect/preterite endings, as well as the most common irregular verb endings. After finishing Spanish review, we continued with physics, in which she has an exam this Friday. Her class is continuing their study of motion, kinematics, and she has moved from uniform motion (linear position, constant velocity) to motion with uniform acceleration (quadratic position, linear velocity, and constant acceleration). Acceleration itself is the change in velocity over a given period of time-- what her class is focusing on specifically is the relationship between position, velocity and acceleration over the same period of time of the same motion of a given object. These relationships, while difficult to see immediately, are fortunately always the same. Graphically, we are always comparing slopes. If given a diagram with some description of motion of an object, we can map the quadratic position function using the diagram itself to see how fast it's initially moving, where it will accelerate, decelerate, stay the same speed or stop. Once we have the position graph, the steps that follow will be the same for every single problem of this sort: we will look at the slope. The velocity graph is drawn as the value of the slope for each corresponding point in time of position. So if at t=1, the slope on the position graph is 4, the velocity at t=1 is 4; this is called instantaneous velocity, or velocity at a specific point in time (different from average velocity, which we have also looked at, which is an average of the entire course of movement of an object). To graph velocity then, we look at how the slope of the position changes and graph accordingly, knowing the velocity will always be linear with uniform acceleration. When we have graphed velocity, we use these same steps listed above to draw our acceleration graph. Because we already know that acceleration is uniform, we know that our graph of acceleration will have 1 or more only horizontal lines-- we graph the slope of velocity in our acceleration graph. She and I went over multiple practice problems to get these methods down, as well as see the different paths of quadratic movement and how it relates to velocity and acceleration. She felt more comfortable with the material, and I encouraged her to look carefully at her review sheet that she will receive the day after our session to make sure that she can do problems of this nature completely on her own and with confidence. I feel very good about her progress, and I am confident that she will do well on her test-- her grade in this class is hovering around B+/A-, and I believe she will push this up moving towards the end of the year."