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Kinematics
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Adjust Merged Sequence — Kinematics

The combined teaching order: statements and actions interleaved, with each learning goal after the last of its components. The initial list is an interleaved stable merge of the statement and action sequences. Drag to adjust (violations are flagged and block Save), then Save Merged Sequence to persist it.

Showing the stable merge of your Step 3 sequences — not yet saved. Adjust if needed, then Save. Changing the per-domain sequences, Assumed Knowledge, or the learning-goal selection resets this page's saved order.

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Position statement
A position is a point in space.
requires: —  ·  required by: Displacement, DistanceTraveled, Velocity
K-12 Physics
Direction statement
Definition of direction, TBD
requires: —  ·  required by: Displacement, Velocity
K-12 Physics
Magnitude statement
Magnitude, or length, is one of the two components of a vector.
requires: —  ·  required by: Displacement, Velocity
K-12 Physics
DistanceTraveled statement
The distance traveled is the length of a specific path between two points. The SI unit for distance traveled is the meter, $\mathrm{m}$.
requires: Position  ·  required by: AverageSpeed
K-12 Physics
TimeInterval statement
A time interval, or time period, is a portion of time that begins and ends at specific instants.
requires: —  ·  required by: Duration
K-12 Physics
Duration statement
A duration is the magnitude of a time interval or time period. The SI unit of duration is the second, $\mathrm{s}$.
requires: TimeInterval  ·  required by: AverageSpeed, Displacement, InstantaneousChange
K-12 Physics
Displacement statement
A displacement is a vector whose length is the shortest distance from an initial to a final position. The SI unit for the magnitude of displacement is the meter, $\mathrm{m}$.
requires: Direction, Duration, Magnitude, Position  ·  required by: AverageVelocity
K-12 Physics
FindVectorSum action
Find the vector sum of an arbitrary number of vectors in arbitrary directions
requires: —  ·  required by: —
K-12 Physics
RepLineGraph action
Represent data in a line graph
requires: —  ·  required by: —
K-12 Physics
ChooseEquation action
Choose the appropriate equation to use to solve for an unknown
requires: —  ·  required by: —
K-12 Physics
RepMotionMap action
Represent one-dimensional motion with a motion map/strobe diagram (dots at equal time intervals)
requires: —  ·  required by: —
K-12 Physics
DrawTangent action
Draw the line that is tangent to a curve at a particular point
requires: —  ·  required by: —
K-12 Physics
FindVectorCompFromMagDir action
Find the component of a vector along an axis, given the vector's magnitude and direction relative to that axis
requires: —  ·  required by: —
K-12 Physics
FindVectorDirFromComp action
Find the direction of a vector with respect to a coordinate axis, given the vector's components in that coordinate system
requires: —  ·  required by: —
K-12 Physics
EvalScalarArith action
Evaluate arithmetic operations on scalars: addition, subtraction, multiplication, and division
requires: —  ·  required by: EvalLineSegmentSlope, EvalPathLength, EvalPowersRoots, FindProductVectorScalar, ManipulateAlgebra
K-12 Physics
FindDispOrderedPair learning goal
Given an object's positions at the beginning and end of a time interval, the student finds the object's displacement during the item interval as an ordered pair $\left(x,y\right)$.
components: Displacement, EvalScalarArith
AverageVelocity statement
An object's average velocity in a time interval is its displacement in the time interval, divided by the duration of the time interval. The SI unit for the magnitude of average velocity is meters per second ($\mathrm{m/s}$).
requires: Displacement  ·  required by: —
K-12 Physics
AverageSpeed statement
The average speed of an object in a time interval is the distance traveled by the object in the time interval, divided by the duration of the time interval. The SI unit for average speed is meters per second ($\mathrm{m/s}$).
requires: DistanceTraveled, Duration  ·  required by: —
K-12 Physics
EvalPathLength action
Evaluate the length of a path comprised of straight segments and/or circular arcs given the necessary coordinate values
requires: EvalScalarArith  ·  required by: —
K-12 Physics
DetAvgSpeed learning goal
Given the path traveled by an object during a time interval, the student determines the object's average speed during that time interval.
components: AverageSpeed, EvalPathLength
InstantaneousChange statement
An instantaneous change in a quantity is the limiting value of the change in the quantity's value, divided by the duration of that change, as the duration approaches zero.
requires: Duration  ·  required by: Velocity
K-12 Physics
Velocity statement
An object's (instantaneous) velocity is the instantaneous rate of change of its position. The SI unit for the magnitude of velocity is meters per second ($\mathrm{m/s}$).
requires: Direction, InstantaneousChange, Magnitude, Position  ·  required by: Acceleration, AverageAcceleration, PosSlopeIsVel, Speed, TopOfFlight
K-12 Physics
Speed statement
An object's (instantaneous) speed is the magnitude of its (instantaneous) velocity vector. The SI unit for speed is meters per second ($\mathrm{m/s}$).
requires: Velocity  ·  required by: ConstantSpeedConstantDist, GreaterSpeedGreaterDist
K-12 Physics
Acceleration statement
An object's (instantaneous) acceleration is the instantaneous rate of change of its velocity. The SI unit for the magnitude of acceleration is meters per second squared ($\mathrm{m/s}^2$).
requires: Velocity  ·  required by: AccelAreaIsVelChange, EarthSurfaceGravAccel, EarthSurfaceGravDir, IndepMotions, KinEqn2_dvt, KinEqn3_dv_plus_at^2
K-12 Physics
AverageAcceleration statement
An object's average acceleration in a time interval is its change of velocity in the time interval, divided by the duration of the time interval. The SI unit for the magnitude of average acceleration is meters per second squared ($\mathrm{m/s}^2$).
requires: Velocity  ·  required by: —
K-12 Physics
EvalLineSegmentSlope action
Evaluate the slope of a line segment
requires: EvalScalarArith  ·  required by: —
K-12 Physics
ManipulateAlgebra action
Manipulate algebraic equations and expressions
requires: EvalScalarArith  ·  required by: SolveAndSub, SolveLinearInVar, SolveQuadraticInVar
K-12 Physics
SolveLinearInVar action
Solve an equation that is linear in a variable to obtain an expression for that variable
requires: ManipulateAlgebra  ·  required by: —
K-12 Physics
SolveQuadraticInVar action
Solve an equation that is quadratic in a variable to obtain an expression for that variable
requires: ManipulateAlgebra  ·  required by: —
K-12 Physics
EvalPowersRoots action
Evaluate numbers raised to powers, including fractional powers (roots)
requires: EvalScalarArith  ·  required by: EvalAlgebraicExpression, FindVectorMagFromComp
K-12 Physics
EvalAlgebraicExpression action
Evaluate an expression (which may be the right-hand side of a suitably-solved equation)
requires: EvalPowersRoots  ·  required by: —
K-12 Physics
FindVectorMagFromComp action
Find the magnitude of a vector, given the vector's components in a coordinate system
requires: EvalPowersRoots  ·  required by: —
K-12 Physics
FindProductVectorScalar action
Find the product or quotient of a vector and a scalar
requires: EvalScalarArith  ·  required by: —
K-12 Physics
FindAvgAccel learning goal
Given velocities of arbitrary magnitudes and directions at the beginning and end of a time interval, the student finds the average acceleration during the time interval.
components: AverageAcceleration, FindProductVectorScalar, FindVectorSum
FindAvgVel learning goal
Given an object's positions at the beginning and end of a time interval, the student finds the magnitude and direction of the object's average velocity during the time interval.
components: AverageVelocity, FindProductVectorScalar, FindVectorDirFromComp, FindVectorMagFromComp
GreaterSpeedGreaterDist statement
In equal time intervals, an object with a greater speed will travel a greater distance than an object with a lesser speed.
requires: Speed  ·  required by: —
K-12 Physics
ConstantSpeedConstantDist statement
An object moving at constant speed will travel equal distances in equal time intervals.
requires: Speed  ·  required by: —
K-12 Physics
KinEqn2_dvt statement
One-dimensional motion with constant acceleration is described by the equation $x_\text{2}=x_\text{1} + \frac{1}{2} (v_\text{1}+v_\text{2}) (t_\text{2}-t_\text{1})$, where $x_\text{2}$ is the position at time $t_\text{2}$, $x_\text{1}$ is the position at time $t_\text{1}$, $v_\text{2}$ is the velocity at time $t_\text{2}$, and $v_\text{1}$ is the velocity at time $t_\text{1}$.
requires: Acceleration  ·  required by: —
K-12 Physics
KinEqn3_dv_plus_at^2 statement
One-dimensional motion with constant acceleration is described by the equation $x_2=x_1 + v_1 (t_2-t_1)+\frac{1}{2} a (t_2-t_1)^2$, where $x_2$ is the position at time $t_2$, $x_1$ is the position at time $t_1$, $v_1$ is the velocity at time $t_1$, and $a$ is the acceleration.
requires: Acceleration  ·  required by: —
K-12 Physics
CalcKinEqn3 learning goal
For an object in one-dimensional motion with constant acceleration, given any four of the initial position $x_1$, final position $x_2$, initial velocity $v_1$, acceleration $a$, and duration $\Delta t = \left(t_2-t_1\right)$, the student calculates the fifth.
components: EvalAlgebraicExpression, KinEqn3_dv_plus_at^2, SolveLinearInVar, SolveQuadraticInVar
SolveAndSub action
Solve an equation for a variable and substitute for that variable in another equation
requires: ManipulateAlgebra  ·  required by: —
K-12 Physics
RepPhenomModel action
Represent a phenomenon using a model
requires: —  ·  required by: —
K-12 Physics
ClassifyEvidence action
Classify a phenomenon based on evidence, not direct observation.
requires: —  ·  required by: —
K-12 Physics
ClassifyRelSpeedMotionMap learning goal
Given several motion maps, or several portions of the same motion map, based on the same duration, the student distinguishes time intervals having lesser, the same, or greater speeds.
components: ClassifyEvidence, ConstantSpeedConstantDist, GreaterSpeedGreaterDist, RepMotionMap
EarthSurfaceGravDir statement
Over a sufficiently small area of Earth's surface, the direction of Earth's gravitational acceleration can be approximated as constant, and defines "down".
requires: Acceleration  ·  required by: ProjectileMotion
K-12 Physics
IndepMotions statement
The component of an object's velocity along an axis is not affected by a component of acceleration along a perpendicular axis.
requires: Acceleration  ·  required by: —
K-12 Physics
TopOfFlight statement
At the highest point of an object's trajectory, the vertical component of the object's velocity is zero.
requires: Velocity  ·  required by: —
K-12 Physics
AccelAreaIsVelChange statement
For an object in one-dimensional motion, on an acceleration v. time graph, the area under the curve between two times (clock readings), is the change of velocity during that time interval.
requires: Acceleration  ·  required by: —
K-12 Physics
ApproximateShape action
Approximate an irregular shape with a simply polygon.
requires: —  ·  required by: —
K-12 Physics
EvalAreaPolygon action
Evaluate the area of a simple polygon
requires: —  ·  required by: —
K-12 Physics
ConstrVelGraphFromAccelGraph1D learning goal
Given an acceleration v. time graph, and an initial velocity, for an object in one-dimensional motion, the student constructs the corresponding velocity v. time graph.
components: AccelAreaIsVelChange, ApproximateShape, EvalAreaPolygon, RepLineGraph
EarthSurfaceGravAccel statement
Near Earth's surface, the magnitude of the gravitational acceleration, $g$, is approximately $9.8 \, \mathrm{m/s}^2$.
requires: Acceleration  ·  required by: ProjectileMotion
K-12 Physics
ProjectileMotion statement
Projectile motion is motion under the influence of only Earth's gravitational acceleration $g$, which is assumed constant in magnitude and direction. This means that the motion must be near Earth's surface, over distances that are small relative to Earth's radius, and air resistance and other forces are assumed to be negligible.
requires: EarthSurfaceGravAccel, EarthSurfaceGravDir  ·  required by: —
K-12 Physics
CalcProjReleasedHorizDist learning goal
For an object in projectile motion, given the altitude at which the object was released and its initial velocity (vector), the student calculates the horizontal distance traveled before the object hits the ground.
components: ChooseEquation, EvalAlgebraicExpression, IndepMotions, KinEqn3_dv_plus_at^2, ProjectileMotion, RepPhenomModel, SolveLinearInVar, SolveQuadraticInVar
DeriveProjLaunchRange learning goal
For an object in projectile motion, launched from and returning to earth's surface, the student derives the equation for the range (horizontal distance traveled) $R=\frac{v_0^2\sin^2 2\theta }{g}$, where $v_0$ is the initial speed, $\theta$ is the launch angle, and $g\approx 9.8\, \mathrm{m/s}^2$ is the acceleration of gravity.
components: FindVectorCompFromMagDir, IndepMotions, KinEqn2_dvt, KinEqn3_dv_plus_at^2, ProjectileMotion, RepPhenomModel, SolveAndSub, TopOfFlight
PosSlopeIsVel statement
For motion in one dimension, the slope of the tangent to the graph of position v. time at a particular time (clock reading) is the instantaneous velocity at that time.
requires: Velocity  ·  required by: —
K-12 Physics
ConstrVelGraphFromPosGraph1D learning goal
Given a position v. time graph for an object in one-dimensional motion, the student constructs the corresponding velocity v. time graph.
components: DrawTangent, EvalLineSegmentSlope, PosSlopeIsVel, RepLineGraph

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This will discard your unsaved changes and return to the last saved merged sequence (or the stable merge, if none is saved). Proceed?

Re-merge from Step 3?

This discards the saved merged sequence (and any unsaved changes) and rebuilds the list from the stable merge of the current Sequence Statements / Sequence Actions orders. Proceed?

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