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:

• 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”

•

• 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

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.

Time (s)

v (m

/s)

Interpreting a Velocity vs. Time Graph

The _______________the curve is the objects displacement.

Interpreting a Velocity vs. Time Graph

The area under the curve is the objects displacement.

Time (s)

v (m

/s)

Interpreting a Velocity vs. Time Graph

The area under the curve is the objects displacement.

Time (s)

v (m

/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 sub-part

• These steps can be a guide for solving problems in this course