UNIT 01 - Kinematics: The Study of Motion 1. Motion in One Dimension A) Students should understand the general relationships among position, velocity, and acceleration for the motion of a particle along a straight line, so that: (1) Given a graph of one of the kinematic quantities-- position, velocity or acceleration as a function of time, students can recognize in what time intervals the other two are positive, negative, or zero; and can identify or sketch a graph of each as a function of time (C 1.1) (2) Given an expression for one of the kinematic quantities-- position, velocity, or acceleration as a function of time, students can determine the other two as a function of time; and find when these quantities are zero or achieve their maximum and minimum values. (C 1.2) B) Students should understand the special case of motion with constant acceleration, so they can: (1) Write down expressions for velocity and position as functions of time, and identify or sketch graphs of these quantities. (B & C 1.3) (2) Use the equations below and to solve problems involving one-dimensional motion with constant acceleration. (B & C 1.4) C) Students should know how to deal with situations in which acceleration is a specified function of velocity and time so they can write an appropriate differential equation and solve it for u by separation of variables, incorporating correctly a given initial value of u. (C 1.5) 2. Motion in Two Dimensions --Including Projectile Motion: A) Students should be able to add, subtract, and resolve displacement and velocity vectors, so they can: (1) Determine components of a vector along two specified, mutually perpendicular axes (C 1.6) (2) Determine the net displacement of a particle or the location of a particle relative to another (B & C 1.7) (3) Determine the change in velocity of a particle or the velocity of one particle relative to another (B & C 1.8). B) Students should understand the general motion of a particle in two dimensions so that, given functions x(t) and y(t) which describe this motion, they can determine the components, magnitude, and direction of the particle’s velocity and acceleration as functions of time (C 1.9) C) Students should understand the motion of projectiles in a uniform gravitational field, so they can: (1) Write down expressions for the horizontal and vertical components of velocity and position as functions of time, and sketch or identify graphs of these components (B & C 1.10). (2) Use these expressions in analyzing the motion of a projectile that is projected with an arbitrary initial velocity (B & C 1.11) SKILLS TO LEARN: 1) Understanding that the instantaneous slope of a function at anytime can yield VERY interesting information: a) Calculating the instaneous slope of a function (aka the derivative of the line) 2) Understanding that the area under a curve can yield very important information (we'll get to that later using integration) TIPS & TOOLS: Download Wolfram Alpha on your phone (if you ahve one) and learn how to use it! STUDY GUIDE: