1 - How Things Move

Free fall

Slope is acceleration ________- 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 objects position on the vertical (y) axis The slope of a position- time graph is the objects 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 objects 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