There are 5 kinematic equations that we will study. KINEMATIC FORMULAS… Let us Pray! Kinematics is the branch of classical mechanics which describes the motion of points (alternatively "particles"), bodies (objects), and systems of bodies without consideration of the masses of those objects nor the forces that may have caused the motion. Kinematics as a field of study is often referred to as the "geometry of motion“ There are 5 kinematic equations that we will study.

But First…. We NEED to get this! Displacement (x, xo); meters (m) Velocity (v, vo); meters per second (m/s) Acceleration (a); meters per s2 (m/s2) Time (t); seconds (s) Review sign convention for each symbol

Distance vs Displacement Distance is the length traveled Displacement is the “straight line” distance from an objects original position (simple terms: How far an object is from its starting point) Variable can be: Base Units d, x, or even y Meters (m) Movement along the x-axis (side to side) Movement along the y-axis (up and down) Δx Δy

V = d/t Speed vs Velocity Speed is the distance traveled per unit time Velocity is the displacement traveled per unit time, including direction Variable can be: Base Units s, v, vf, vi, vo Meters/second (m/s) Velocities can be both positive and negative depending on the DIRECTION of Motion V = d/t

A= Vf-Vo t Acceleration Acceleration is the change in velocity over time. Variable can be: Base Units a Meters/second2 (m/s2) Acceleration can be positive (speeding up) or negative (slowing down). Acceleration can sometimes be IMPLIED. Free fall questions automatically have an acceleration of -9.8m/s2 due to gravity. A= Vf-Vo t

The Signs of Displacement Displacement is positive (+) or negative (-) based on LOCATION. The Signs of Velocity Velocity is positive (+) or negative (-) based on direction of motion. Acceleration Produced by Force Acceleration is (+) or (-) based on direction of force (NOT based on v).

Before we Start…. Distance (can be “x” or “d”); meters (m) Can also be “y” if something is moving up/down Velocity (v, vo , vi); meters per second (m/s) Acceleration (a); meters per s2 (m/s2) Time (t); seconds (s) From now on, speed and velocity will be treated the same. From now on, distance and displacement will be treated the same. Velocity (Speed) = distance time Acceleration = Vfinal – Vinitial time

Kinematic Equations Δx = ½ (Vi + Vf)•t Vf = Vi + at Δx = Vi• t + ½ at2 Vf2 = Vi2 + 2aΔx Δx = Vf• t - ½ at2 Vi = Initial Velocity (m/s) Vf = Final Velocity (m/s) a = Acceleration (m/s2) t = Time (s) Δx = Distance (m)

How to choose the right Equation KINEMATICS Vi Vf t a Δx Δx = ½ (Vi + Vf)•t Vf = Vi + at Δx = Vi• t + ½ at2 Vf2 = Vi2 + 2aΔx Δx = Vf• t - ½ at2 NO NO NO NO NO

Problem Solving Strategy Read the problem Draw diagram of your problem (if needed) Identify your GIVENS Identify your Unknown Choose and equation Manipulate (if necessary) to solve for variable Plug in and solve - PEMDAS!! Answer with units

Δx = Vf• t - ½ at2 Δx = ½ (Vi + Vf)•t No Initial Velocity!!! No Acceleration!! Δx = ½ (Vi + Vf)•t

Example Vf2 = Vi2 + 2aΔx 352 - 102 = a - Vi2 - Vi2 (2●3000) What is the acceleration of a car that has an original velocity of 10 m/s that accelerates for 3000 m and reaches a final velocity of 35 m/s? Given: Vi = 10 m/s Vf = 35 m/s Δx = 3000m Find: a = ?? Vf2 = Vi2 + 2aΔx 352 - 102 = a - Vi2 - Vi2 (2●3000) Vf2 - Vi2 = 2aΔx 2Δx 2Δx 0.1875 m/s2= a Vf2 - Vi2 = a 2Δx