Kinematics (1-d)
Mr. Austin
Motion
• ______________is the classification and comparison of
an objects motion.
• Three “rules” we will follow:
– The motion is in a _________________
– The ___________of the motion is ignored (coming soon!)
– The _____________considered is a particle (not for long!)
• Particles and particle like objects move uniformly
– Ex. A sled going down a hill
– ANTI Ex. A ball rolling down a hill
Position
• The _______________of the particle in space.
• Needs a mathematical description to be useful.
• We assign a number to represent the particles
position on a ________________grid.
– There needs to be a ____________point to reference
– The positions to the left are _____________
– The positions to the right are _______________
Vectors (more to come)
• A vector is a mathematical representation of
something that has:
– Size
– _______________
• A scalar is a mathematical representation of something
that has only size, but no _____________.
• Direction is represented mathematically using a variety
of methods.
– Angles
– _______________________
– Algebraic signs
Displacement
• Displacement is the change in a particles
______________
• It is a vector quantity
– Has a size
– Has a direction
• SI unit of: ____________(m)
• Mathematically displacement is:
_______________________________
Sample Problem
• What is the displacement of a car that starts
at x = 5 meters and ends at x = -3 meters?
• What is the displacement of a car that starts
at x = -10 meters and ends at x = -12 meters?
Challenge
• What is your displacement if you run one lap
on a round 400m track?
Displacement vs. Distance
• ___________________is only concerned with
the difference between the starting point and
ending point. It is a vector.
• _______________is the total length an object
covers. It is a scalar.
Sample Problem
• What is the distance and displacement, from
position A (25m) to F (-55m), of the car?
Distance
Displacement
Plotting an Objects Position with Time
Average Velocity
• The ______________at which the position of an object
changes with time
• It is a vector
– Has a magnitude
– Has a direction
• SI unit: meter/second (m/s)
• Mathematically:
___________________________
• This is the ________________of a position time graph
Sample Problem
• What is the average velocity if you run the
length of football field (91.4 meters) in 20
seconds?
Challenge
• What is the average velocity if you
circumnavigate the globe in 3 days?
Average Speed
• The rate that a _____________is covered relative
to time
• It is a scalar.
• Unit: m/s
• Mathematically:
distance
savg =
time
• Challenge: Can average speed and average
velocity be the same? Can they be different?
Sample Problem
• A car pulls out of a driveway and goes 5
meters forward than reverses 3 meters. All of
this happens in 8 seconds. What is the average
speed and velocity of the car?
Average Speed
Average Velocity
Book Practice for Homework
• Page 29 #1
• Page 30 #1, 2, 3, 5, 8
Instantaneous Velocity
• Mr. Austin traveled from Garnet Valley High
School’s parking lot to the Franklin Institute
(24.2 miles) in 42 minutes. What was Mr.
Austin’s average speed?
• __________________velocity is the velocity
of a particle at any given moment in time.
– Can be positive, negative, or zero.
Instantaneous Velocity, graph
• The instantaneous
velocity is the slope of
the line __________to
the x vs. t curve
• This would be the
green line
• The light blue lines
show that as t gets
smaller, they approach
the green line
Average Speed vs Speed
• Average speed is the distance traveled divided
by the time it takes to travel. Its is a scalar.
• Speed is simply the _________________of
instantaneous velocity.
– Strip the velocity of any direction information
– It is a scalar
Acceleration
• The change in velocity of an object.
• It is a vector
– Has a size
– Has a direction
• Unit: _________
• Average ________________is represented
mathematically as:
______________________________
Instantaneous Acceleration -graph
• The _________of the
velocity-time graph is the
acceleration
• The green line represents
the instantaneous
acceleration
• The blue line is the
average acceleration
Graphical Comparison
• Given the displacement-time graph (a)
• The velocity-time graph is found by measuring the slope of
the position-time graph at every instant
• The acceleration-time graph is found by measuring the slope
of the velocity-time graph at every instant
Viewing Acceleration
Acceleration Expressed in g’s
– When accelerations are _________we express
them as a multiple of “g”
• g = 9.8 m
s2
• It is the acceleration due to gravity near the surface of
the Earth
– A man starts from rest and is accelerated to the
speed of sound (340.2 m/s) on a rocket sled. This
occurs in .75 seconds. What is his acceleration in
terms of g?
Constant Acceleration
• This is a special case that tends to simplify things.
• Constant, or _________________, acceleration
occurs all the time.
– Car starting from rest when a light turns green
– Car braking at a light when a light turns red
• There are a set of equations that are used to
describe this motion.
Kinematic Equations
Constant Acceleration Problem
• A car starts from rest and accelerates
uniformly to 23 m/s in 8 seconds. What
distance did the car cover in this time?
Book Practice
• Page 31 #22, 24, 28, 30
Graphical Look at Motion:
displacement – time curve
• The __________of the
curve is the velocity
• The curved line
indicates the
___________is
changing
– Therefore, there is an
acceleration
Graphical Look at Motion:
velocity – time curve
• The slope gives the
____________
• The straight line
indicates a constant
_______________
Graphical Look at Motion:
acceleration – time curve
• The zero slope indicates a
___________acceleration
Test Graphical Interpretations
• Match a given velocity graph with the
corresponding acceleration graph
Free Fall Acceleration
• This is a case of constant acceleration that occurs
___________________.
• All things fall to the Earth with the same acceleration
– In the absence of ________________________, all things
fall to the Earth with the same acceleration:
_____________________
– This is invariant of the objects dimensions, density, weight
etc.
• When using the kinematic equations we use
– ay = -g = -9.80 m/s2
m
g ¹ -9.8 2
s
Free Fall – an object dropped
• Initial velocity is
_______
• Let up be positive
• Use the kinematic
equations
– Generally use y instead
of x since vertical
• Acceleration is
– ay = -g = -9.80 m/s2
vo= 0
a = -g
Free Fall – an object thrown
downward
• ay = -g = -9.80 m/s2
• Initial velocity ____0
– With upward being
positive, initial velocity
will be negative
vo≠ 0
a = -g
Free Fall -- object thrown
upward
• Initial velocity is upward, so
positive
• The
______________velocity at
the maximum height is zero
• ay = -g = -9.80 m/s2
everywhere in the motion
v=0
vo≠ 0
a = -g
Thrown upward, cont.
• The motion may be symmetric
– Then tup = tdown
– Then v = -vo
• The motion may not be symmetric
– Break the motion into various parts
• Generally up and down
Free Fall Example
• Initial velocity at A is upward (+) and
acceleration is -g (-9.8 m/s2)
• At B, the velocity is 0 and the acceleration
is -g (-9.8 m/s2)
• At C, the velocity has the same magnitude
as at A, but is in the opposite direction
• The displacement is –50.0 m (it ends up
50.0 m below its starting point)
Vertical motion sample problem
• A ball is thrown upward with an initial velocity of 20 m/s.
– What is the max height the ball will reach?
– What will the velocity of the ball be half
way to the maximum height?
– What will the velocity of the ball be half
way down to the hand?
– What is the total time the ball is in the air?
Book Practice
• Page 32 # 43, 47, 51.
Interpreting a Velocity vs. Time
Graph
v (m/s)
The _______________the curve
is the objects displacement.
Time (s)
Interpreting a Velocity vs. Time
Graph
The area under the curve is the
objects displacement.
v (m/s)
Þ Dx = Dt × v
Time (s)
Interpreting a Velocity vs. Time
Graph
v (m/s)
The area under the curve is the
objects displacement.
1
area = bh+l × w
2
Time (s)
General Problem Solving Strategy
•
•
•
•
Conceptualize
Categorize
Analyze
Finalize
Problem Solving – Conceptualize
• Think about and understand the situation
• Make a quick drawing of the situation
• Gather the numerical information
– Include algebraic meanings of phrases
• Focus on the expected result
– Think about units
• Think about what a reasonable answer should be
Problem Solving – Categorize
• Simplify the problem
– Can you ignore air resistance?
– Model objects as particles
• Classify the type of problem
– Substitution
– Analysis
• Try to identify similar problems you have
already solved
– What analysis model would be useful?
Problem Solving – Analyze
•
•
•
•
Select the relevant equation(s) to apply
Solve for the unknown variable
Substitute appropriate numbers
Calculate the results
– Include units
• Round the result to the appropriate
number of significant figures
Problem Solving – Finalize
• Check your result
– Does it have the correct units?
– Does it agree with your conceptualized ideas?
• Look at limiting situations to be sure the
results are reasonable
• Compare the result with those of similar
problems
Problem Solving – Some Final
Ideas
• When solving complex problems, you may
need to identify sub-problems and apply
the problem-solving strategy to each subpart
• These steps can be a guide for solving
problems in this course