Unit 1 Kinematics

Constant Velocity Model Concepts

• The paradigm (“pattern”) for this unit is the buggy.  We observed the buggy traveling in a straight line (mostly), and covering equal amounts of distance in equal times.  Upon examination of the motion of the buggy, we described it as constant velocity.
• In order to measure lengths or positions, we must pick a reference point.  Once we’ve picked a reference point, we generally call it “zero,” and define to the left of the reference point as the negative direction (negative positions) and to the right of the reference point as the positive direction (positive positions). 
• Displacement (often written ) is the change in position from a reference point.  Displacement is a vector, meaning it has a magnitude (size) and a direction (often simply positive or negative).
• Distance is how far you travel.  It is a scalar because it has only a size, no direction.  It is of less use in accurate descriptions of motion, so in physics we concentrate on displacement.
• What we commonly call time can be described in two ways, a clock reading (you note what time the clock displays for an instant), and a time interval (delta t, or final time-initial time).  How long does 12 noon last?
• An instant is an infinitesimally small amount of time.  It is the amount of time that passes in a clock reading.
• An object can cover distance while ending up without displacement, if it returns to its starting point at the end of the time interval.
• Average Speed is defined as total distance over total time.  It is a scalar.
• Average Velocity (v with a “bar” over it) is defined as the displacement over the time interval, .  It is a vector because displacement is a vector.  Thus it has a magnitude and a direction. 
• Instantaneous velocity is the velocity at an instant. Instantaneous speed is what your car’s speedometer shows.
• An object with constant velocity (the buggy, for example), always has an average velocity equal to its instantaneous velocity.
• The velocity is the slope of a linear pos-t graph.  If the velocity is constant, the pos-t graph must be linear ( it has one slope/velocity).
• A linear pos-t graph can be modeled with an equation of the form y=mx + b
• The intercept of the pos-t graph represents the initial velocity.
• A linear pos-t graph implies a constant velocity-time graph (v-t graph).  A constant graph is a horizontal line.
• The area of a vel-t graph is the displacement.
• The vel-t graph does not tell us anything about starting and ending positions, only about displacement.

Constant Acceleration Model Concepts

• The paradigm for this unit is an object rolling down a ramp or the fan cart.  As the object travels down the ramp, it gains more position in equal intervals of time (it speeds up).  We found that the velocity of the object changed by equal amounts in equal time intervals.  Upon examination of the motion of the object, we defined it as constant acceleration.
• Average Acceleration is defined as the change in velocity over the change in time .  It is a vector and is the slope of the v-t graph. 
• Acceleration is a rate of change of a rate of change.  An object that accelerates at 9.8 m/s² or m/s/sgains 9.8 m/s of velocity for every second it accelerates.
• If the pos-t graph is a curve, the object is accelerating.  Curves that we see (to describe motion in this class) usually fit a power regression (to the second power) or a quadratic regression.  Each term in the regression equation has some physical meaning.  The shape of these curves is parabolic.  The form of the model for an object undergoing constant acceleration is y=Ax²+Bx+C.
• If the pos-t graph is a curve, the slope of a tangent line to the curve is the instantaneous velocity at that point on the graph (the velocity at that moment).
• The intercept of the pos-t graph is once again the initial position.  
• When an object undergoing constant acceleration changes direction, its instantaneous velocity is zero.  However, its acceleration is not zero.
• If the v-t graph is a curve, the acceleration is changing.  The slope of the tangent line is the instantaneous acceleration for this graph.
• A positive acceleration makes something traveling in the positive direction speed up, and an object traveling in the negative direction slows down.  A negative acceleration makes something traveling in the negative direction speed up, and an object traveling in the positive direction slows down.
• Deceleration is when an object is slowing down (speed is going toward zero).  It is not the same thing as a negative acceleration (which can represent speeding up in a negative direction).
• Working from the definitions above, we can derive useful equations that describe the motion of objects.
• In a vacuum, all falling objects accelerate at the same rate.  The shorthand for this rate is g (the value of g on Earth is 9.8 m/s² but we often round that value to 10 so that we can do calculations in our heads.
• Objects accelerate at the same rate on earth b/c even though more massive objects experience a greater pull of earth’s gravity (or weight), their mass (or inertia) resists that pull.  Air resistance interferes with this fact in the atmosphere.
• The effect of air resistance is more important as objects have the following characteristics: lighter, more surface area, less aerodynamic shape, moving faster.  We will usually ignore air resistance b/c it makes the math easier, but for more accurate results, it must be included in many cases.
• An object undergoes freefall when only the force of earth’s gravity is acting on it in a significant way.  Anything thrown up or down, or dropped qualifies as freefalling from the instant it is released. 
• The instantaneous velocity of an object tossed up is zero at the top of its path.  Its acceleration is g.
• The speed at equal altitudes of an object tossed up is equal.  The velocities are opposites (one is traveling up, the other is down).

SKILLS

Topic 1.1 Scalars and Vectors in One Dimension
Skill	Resource
Graphical Vector addition and subtraction	PhET Vector Addition (use “Equations” tab for subtraction
Topic 1.2 Displacement, Velocity, and Acceleration
Skill	Resource
Basic kinematics, Reference Frame, Position, Path Length, and Displacement	fysicsfool YouTube Video
Topic 1.3 Representing Motion
Skill	Resource
Graphing a scatter plot with best-fit	fysicsfool YouTube Video
Creating a motion map from a x-t graph	fysicsfool YouTube Video
Creating motion maps by observation	Duffy Motion Diagram Simulation
Linearizing a quadratic function graph	fysicsfool YouTube Video
Writing equations for data graphs	fysicsfool YouTube Video
Calculating displacement (“delta x“) from a velocity-time graph	fysicsfool YouTube Video
Calculus Introduction to the derivative (calculating and interpreting the slope of a tangent line on a position-time graph)	fysicsfool YouTube Video
Calculus Definition of the derivative interactive	Geogebra Interactive
Topic 1.4 Reference Frames & Relative Motion
Skill	Resource
Visualizing motion from different reference frames	PSSC Frames of Reference Video (about 30 minutes, first 8 minutes most important)
Topic 1.5 Motion in Two or Three Dimensions
Graphical Vector addition and subtraction	PhET Vector Addition (use “Equations” tab for subtraction