Uniform Accelerated Motion Kinematic Equations Measuring Techniques Assess. Statements – 2.1.5, – Due on Wednesday, Oct. 29

Uniform Accelerated Motion Acceleration: Acceleration: The rate at which an object’s velocity changes The rate at which an object’s velocity changes Units = m·s -2 Units = m·s -2

Measuring Acceleration Experimentally 1 example: Photogates: Like you did in this lab, photogates can be used to determine the time it takes an object to travel a short distance, therefore you can determine instantaneous velocities 2 photogates allow you to determine an initial velocity, a final velocity, and a total time between the two.

Kinematic Equations Kinematic Equations are considered to be “equations of motion” and are based on the fundamental definitions of average velocity and acceleration: Kinematic Equations are considered to be “equations of motion” and are based on the fundamental definitions of average velocity and acceleration:

Our variables There are 5 basic variables that are used in any motion-related calculation: There are 5 basic variables that are used in any motion-related calculation: Initial Velocity = v 0 or v i or v 1 or u Initial Velocity = v 0 or v i or v 1 or u Final Velocity = v or v f or v 2 Final Velocity = v or v f or v 2 Acceleration = a Acceleration = a Displacement = d (sometimes also s or could be  x ) Displacement = d (sometimes also s or could be  x ) Time = t Time = t Bold face indicates a vector Bold face indicates a vector Each of the kinematic equations will use 4 of these 5 variables Each of the kinematic equations will use 4 of these 5 variables

Each of the kinematic equations starts with a rearranged version of the equation for average velocity: And uses substitution, rearranging, and simplifying the equations to get to the end result. For example… Deriving the Equations

Kinematics Equation #1 Step 1: Step 1: Step 2: Substitute equation for Step 2: Substitute equation for Step 3: Rearrange acceleration equation to solve for t, then substitute Step 3: Rearrange acceleration equation to solve for t, then substitute Step 4: Simplify by multiplying fractions Step 4: Simplify by multiplying fractions Step 5: Rearrange Step 5: Rearrange → →

Kinematics Equation #2 Step 1: Step 1: Step 2: Substitute Step 2: Substitute Step 3: Rearrange acceleration equation to solve for v, then substitute Step 3: Rearrange acceleration equation to solve for v, then substitute Step 4: Simplify Step 4: Simplify Step 5: Distribute the t through the equation Step 5: Distribute the t through the equation Step 6: Simplify again Step 6: Simplify again → →

Summary of Equations You will NOT be required to memorize these You will NOT be required to memorize these

Problem Solving Strategy When given problems to solve, you will be expected to “show your work” COMPLETELY! When given problems to solve, you will be expected to “show your work” COMPLETELY! “Showing work” means that you will be expected to include the following pieces in your full answer (or you will not receive full credit for the problem…) “Showing work” means that you will be expected to include the following pieces in your full answer (or you will not receive full credit for the problem…) List of variables – include units on this list List of variables – include units on this list Equation – in variable form (no numbers plugged in yet) Equation – in variable form (no numbers plugged in yet) If necessary, show algebra mid-steps (still no numbers) If necessary, show algebra mid-steps (still no numbers) Plug in your value(s) for the variables Plug in your value(s) for the variables Final answer – boxed/circled with appropriate units and sig figs 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 = u = t = a = Practice Problem #1 25 m/s 0 m/s 3.0 s ? a = -8.3 m / s 2

Practice Problem #2 An airplane starts from rest and accelerates at a constant 3.00 m/s 2 for 30.0 s before leaving the ground. 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 = u = t = a = s = 0 m / s ? 30.0 s 3.00 m / s 2 s = 1350 m ? v = 90.0 m / s