1 How Things Move 1.1 Vocabulary • Position -Where an object is, relative to another (usually the origin or some other zero-point) • Speed -How fast an object is moving • Acceleration -The rate of change of an object’s speed • Displacement -The change in an object’s position from start to finish, excluding any other motion made • Position-Time Graph -A graph where time is on the x-axis and position is on the y-axis. Slope is speed • Velocity-Time Graph -A graph where time is on the x-axis and velocity is on the y-axis. Slope is acceleration • Free fall -Described motion where the only force acting on an object is gravity and its x velocity is 0 • Projectile Motion -Described motion where the only force acting on an object is gravity and its x velocity is non-zero but constant The five most important motion variables are: • v0 -Initial velocity • vf -Final velocity • ∆x -Displacement • a -Acceleration • t -Time If you know three of the five, you can use your equations to find the last two 1.2 Graphical Analysis of Motion • A common mistake is people confuse position-time and velocity-time graphs, DO NOT DO THIS • A position-time graph gives an object’s position on the vertical (y) axis • The slope of a position-time graph is the object’s speed – Steeper slope means the object is moving faster – If the slope is positive, the object is moving forward – If the slope is negative, the object is moving backward • You may not know the exact slope of a position-time graph, just use your best guess – Questions that ask for this want to see that you get the basic idea, not the exact answer • On a velocity-time graph, the object’s speed is given on the vertical (y) axis • The direction of motion on a velocity time graph is given by the sign of the vertical coordinate at any point in time • The acceleration of an object is given by the slope of its velocity-time graph • It is important to note that acceleration does not tell you if something is speeding up or slowing down – If something is moving backwards and has a negative acceleration, it is speeding up in the negative direction – Be careful not to make assumptions, only draw conclusion from information you know definitively • The area between a velocity-time graph and the horizontal axis gives the displacement of an object, which only tells you how far an object ended up from its starting position, NOT where it ends up 1.3 Algebraic Analysis of Motion Algebraic analysis is different from geometric analysis in that you are given a description of a problem. The most important things to extract from this description are: • A positive direction • What you know • What you do not know • What you WANT to know • A start and end time A good strategy is to make a table of known and unknown values with the same five variables from the previous section to better organize your problem solving. Caltulate the missing variables with the kinematic equations: • vf = v0 + a ∗ t • ∆x = v0 ∗ t + ∗ a ∗ t21 2 • v = v + 2 ∗ a ∗ ∆x2 0 2 f 1.4 Free Fall and Projectile Motion • Remember that objects in free fall always have acceleration due to gravity, usually rounded to -10m/s2 in the vertical direction, and no horizontal velocity or acceleration • Objects in projectile motion have two velocities, a horizontal velocity that remains constant and a vertical velocity that changes due to gravity. This means you should have two tables of known and unknown variables for objects in projectile motion, one for each velocity • The two velocities for projectile motion also use the same variable for time as they describe the same object, just in different directions. They must use the same variable for time • The final velocity of an object in free fall or projectile motion is not 0, that is its velocity once it is at rest • The true final velocity is the object’s velocity the instant before it hits the ground