Motion in One Dimension

 

Dimensional Analysis

Definition and use of units to show that free-fall time is proportional to √(h) and 1/√(g).

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Free-fall Experiment

Measurements of falling times for different heights and comparison to dimensional analysis.

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Average Speed and Velocity

Definitions and distinctions between the two, using graph on board.

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Instantaneous Speed and Velocity

Definition of instantaneous velocity using tangent line to a graph, and of instantaneous speed using velocity from graph.

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Bullet Time

Average velocity example using bullet in demonstration.

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Acceleration

Average acceleration equation with example and two short demos; acceleration as v' and x''; and finding sign of acceleration from a graph.

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Definition of average acceleration; definition of instantaneous acceleration, with examples; uniformly accelerated motion, with examples.

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Finding acceleration as a function of time from equations for position.

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General 1D Motion Equation

Kinematics equations for x, v, and a for constant a; example using gravity.

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1D Free-fall Demonstration

Free-fall of object, using strobe-lighting of 2 frequencies to show increasing v.

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Vectors

Distinction between vectors and scalars; addition and subtraction of vectors.

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Decomposition of Vectors

Decomposition of 3D vector into components and use of angles θ and φ with example.

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Dot Product

Dot product formulas using components and using cos(θ), with two brief examples.

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Cross Product Using Determinants

Calculation of the cross product using the determinant of a component matrix, with the determinant explicitly expanded.

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Cross Product Using Corkscrew

Cross product calculation using sin(θ); finding direction by corkscrew method; and importance of right-handed coordinates.

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Dot Product and Cross Product

Definition of dot product, with example; properties of cross products.

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Velocity in Kinematics Problems

Average velocity in 1D kinematics; constructing velocity graph from x vs. t.

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Velocity

Ideal particle simplification; definition of average velocity, with examples; definition of instantaneous velocity, with examples; uniform linear motion; speed of rifle bullet example.

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Acceleration of Gravity

Definition, including equation of motion due to gravity, with examples.

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One-Dimensional Kinematics

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Calculating v(t) and a(t) from x(t); interpreting zeroes of x, v, and a; and graphing x vs. t.

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Worked example of kinematics problem; determining x, v, and a at all times from graph of x vs. t.

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10-part 1D kinematics problem; finding and graphing x, v, a.

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Relative velocity and acceleration defined; special case of constant acceleration.

Displacement, velocity, and acceleration of objects moving in one dimension. Solution not included.

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4-part problem; finding position, acceleration, and average speed from v vs. t. Solutions are given below the problems.

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Constant Acceleration

Area under acceleration vs. time graph; area under velocity vs. time graph; velocity as the integral of acceleration; position as the integral of velocity, with example.

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Dimensions of Displacement

Showing consistency of dimensions, and finding new dimensions for scaled-up equation.

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Half Time vs. Half Distance

5-part 1D kinematics; one person walks half time and runs the other; the other person walks half distance and runs the other.

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Acceleration Curves

Sketching velocity curves within displacement and acceleration parameters.

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Collision of Dropped Balls

3-part problem; graphing and finding time to collision for balls dropped consecutively.

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Car and Motorcycle

One dimensional motion of two vehicles.

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Displacement

Comparing the displacement of an object and its distance traveled. Solution not included.

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Vertical Motion

Motion of a ball thrown vertically. Solution not included.

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Position and Velocity

Determining velocity from a position vs. time graph. Solution not included.

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Relative Velocity

Difference in speed between two falling stones. Solution not included.

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Relative Position

Difference in position between two falling stones. Solution not included.

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Falling Stones

Time interval between two falling stones hitting the ground. Solution not included

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Falling Balls

Velocities of two vertically thrown balls. Solution not included.

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Kinematics

Relative motion of two falling stones.

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Measurement of g

Measuring the acceleration of gravity by timing a falling ball.

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One-Dimensional Kinematics: Track Event

Motion of two runners in a race.

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Relative Inertial Frames

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Motion of a falling object in an elevator viewed from multiple reference frames.

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Plane Round-Trip

Calculating travel time dependent and independent of wind.

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Airplane Against Wind

3-part problem; calculating time for round trip, average velocity, and average speed. Solutions are given below the problems.

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Motion in One-Dimension

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Position, velocity, and acceleration of a runner.

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Definition of kinematics; coordinate system in one dimension; definitions of position, displacement, average velocity, instantaneous velocity, average acceleration, instantaneous acceleration.

Modelling the motion of a person catching a streetcar.

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Slowing a Speeding Car

Motion of two cars, one at constant velocity and the other decelerating.

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Rocket Flight

Vertical motion of a rocket.

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Jumping Man

Motion of and forces acting on a jumping basketball player.

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Space Shuttle

Average speed of a space shuttle during fuel consumption.

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3D and 1D Kinematics

3-part 3D kinematics and 2-part 1D kinematics problem about a moving particle.

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Velocity and Acceleration

6-part 1D kinematics of moving particle involving calculation and graphing of velocity and acceleration.

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