K INEMATIC E QUATIONS New equations and how to use them!

D EFINITIONS Kinematics – Effect of Motion Study and description of motion – without regard to the cause. Dynamics – Cause of Motion

K INEMATIC E QUATIONS Equations of motion Based on the fundamental definitions of average velocity and average acceleration: Arithmetic Mean Plugging in def of Δ

O UR VARIABLES There are 5 basic variables that are used in any motion-related calculation: Initial Velocity = v 0 or v i Final Velocity = v or v f Acceleration = a Displacement = Δx Time = t Bold face indicates a vector Each of the kinematic equations will use 4 of these 5 variables

How far does an object travel during uniformly accelerated motion? W HAT CAN WE DETERMINE ? Rearrange… Substitute… Start

W HAT CAN WE DETERMINE ? Rearrange … Substitute … Continue To… Distribute Δt … Combine like terms …

Can we relate v, a, & Δx without a time variable? W HAT CAN WE DETERMINE ? Rearrange … Substitute into… Start To get..

W HAT CAN WE DETERMINE ? Start Substitute… To get.. Multiply binomials… Solve for v f …

S UMMARY OF E QUATIONS You will NOT be required to memorize these No Time No Position

The equation of the position vs. time graph is: The slope of this graph = velocity The y-intercept of this graph = initial position L AB C ONNECTION : B UGGY L AB

The equation of the velocity-time graph is: The slope of this graph = acceleration The y-intercept of this graph = initial velocity L AB C ONNECTION : GIP’ ER L AB

E QUATIONS THAT DESCRIBE OBJECTS THAT CHANGE THEIR VELOCITIES : Equations from data Linear Graphs from Lab General Equation X vs. t 2 V vs. t V 2 vs. X

P ROBLEM S OLVING S TRATEGY Show your work – ALWAYS! Sketch of situation, motion map, x vs. t plot Use three step method: Equation in variable form (no numbers plugged in yet) If necessary, show algebra mid-steps (still no numbers) Equation with value(s) for the variables (numbers!) Final answer : boxed/circled with appropriate units and sig figs

A school bus is moving at 25 m/s when the driver steps on the brakes and brings the bus to a stop in 3.0 s. What is the average acceleration of the bus while braking? v f = v i = Δ t = a = P RACTICE P ROBLEM #1 25 m/s 0 m/s 3.0 s ? a = -8.3 m / s 2

P RACTICE P ROBLEM #2 An airplane starts from rest and accelerates at a constant 3.00 m/s 2 for 30.0 s before leaving the ground. (a) How far did it move? (b) How fast was it going when it took off? v f = v i = Δ t = a = Δx = 0 m / s ? 30.0 s 3.00 m / s 2 Δx = 1350 m ? v = 90.0 m / s