Kinematic Equations Measuring Techniques Assess Statements 211 215 217 2110 Due on Wednesday Oct 29 Uniform Accelerated Motion Acceleration The rate at which an objects velocity changes ID: 498610
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Slide1
Uniform Accelerated Motion
Kinematic Equations
Measuring Techniques
Assess
. Statements
2.1.1 –
2.1.5,
2.1.7 –
2.1.10
Due on Wednesday,
Oct. 29Slide2
Uniform Accelerated Motion
Acceleration:
The rate at which an object’s velocity changesUnits = m·s-2Slide3
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 velocities2 photogates allow you to determine an initial velocity, a final velocity, and a total time between the two.Slide4
Kinematic Equations
Kinematic Equations are considered to be “equations of motion
”
and are based on the fundamental definitions of average velocity and acceleration:Slide5
Our variables
There are
5
basic variables that are used in any motion-related calculation:Initial Velocity =
v0 or
v
i
or
v
1
or
u
Final Velocity = v or
vf or v
2Acceleration = 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 variablesSlide6
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
EquationsSlide7
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
fractionsStep 5: Rearrange
→
→Slide8
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
→
→Slide9
Summary of Equations
You will NOT be required to memorize these
Slide10
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 figsSlide11
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
2Slide12
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.(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