Uniform Accelerated Motion

Kinematic EquationsMeasuring Techniques

Assess. Statements 2.1.1 – 2.1.5, 2.1.7 – 2.1.10Due on Wednesday, Oct. 29

Uniform Accelerated Motion

Acceleration: The rate at which an object’s velocity

changes Units = m·s-2

t

vv

t

va if

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:

t

dv

t

vva 0

2

0vvv

Our variables

There are 5 basic variables that are used in any motion-related calculation: Initial Velocity = v0 or vi or v1 or u Final Velocity = v or vf or v2 Acceleration = a Displacement = d (sometimes also s or could be Dx) Time = t

Bold face indicates a vector 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…

tvs

Deriving the Equations

Kinematics Equation #1

Step 1: Step 2: Substitute

equation for Step 3: Rearrange

acceleration equation to solve for t, then substitute

Step 4: Simplify by multiplying fractions

Step 5: Rearrange

tvs

tuv

d

2

a

uvuvs

2

v

a

uvs

2

22

222 uvas

asuv 222

2

uvv

→

→a

uvt

Kinematics Equation #2

Step 1:

Step 2: Substitute Step 3: Rearrange

acceleration equation to solve for v, then substitute

Step 4: Simplify Step 5: Distribute the t through the equation

Step 6: Simplify again

tvs

tuv

s

22

uvv

→

atuv tuatu

s

2

)(

tatu

s

2

2

2

2 2atuts

2

2

1atuts

→

Summary of Equations

You will NOT be required to memorize these

atuv

2

2

1atuts

asuv 222

Problem Solving Strategy

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…) List of variables – include units on this list Equation – in variable form (no numbers plugged in

yet) If necessary, show algebra mid-steps (still no

numbers) Plug in your value(s) for the variables 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/s2

atuv

t

uva

atuv

s0.3s

m250 sm

a

Practice Problem #2 An airplane starts from rest and

accelerates at a constant 3.00 m/s2 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/s2

s = 1350 m?

v = 90.0 m/s

2

2

1atuts

2)0.30)(00.3(2

10s

atuv )0.30)(00.3(0v