# Motion in One Dimension

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## Video Clips

#### Dimensional Analysis

RealVideo®
4:47 minutes (22:15 - 27:02)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Units, scaling

#### Free-fall Experiment

RealVideo®
10:23 minutes (27:02 - 37:25)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Uncertainty

#### Average Speed and Velocity

RealVideo®
6:56 minutes (0:00 - 6:56)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Instantaneous Speed and Velocity

RealVideo®
4:08 minutes (6:56 - 11:04)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Speed and velocity

#### Bullet Time

RealVideo®
6:29 minutes (11:04 - 17:33)

Average velocity example using bullet in demonstration.

Instructor: Prof. Walter Lewin
Prior Knowledge: Speed and velocity

#### Acceleration

RealVideo®
9:46 minutes (17:36 - 27:22)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Speed and velocity

#### Worked 1D Kinematics Example

RealVideo®
6:56 minutes (27:22 - 34:18)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Acceleration (17:36 of V2)

#### General 1D Motion Equation

RealVideo®
7:02 minutes (34:18 - 41:20)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: 1D Kinematics (27:22 of V2)

#### 1D Free-fall Demonstration

RealVideo®
9:48 minutes (41:20 - 51:08)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Dimensional Analysis (22:15 of V1), 1D Motion Equations (34:18 of V2)

#### Vectors

RealVideo®
7:54 minutes (0:00 - 7:54)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Decomposition of Vectors

RealVideo®
5:49 minutes (7:54 - 13:43)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Vectors (beginning of V3)

#### Dot Product

RealVideo®
5:59 minutes (13:43 - 19:42)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Decomposition of Vectors (7:54 of V3)

#### Cross Product Using Determinants

RealVideo®
3:48 minutes (19:42 - 23:30)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Decomposition of Vectors (7:54 of V3)

#### Cross Product Using Corkscrew

RealVideo®
6:49 minutes (23:30 - 30:19)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Cross Product Using Determinants (19:42 of V3)

#### Dot Product and Cross Product

RealVideo®
7:12 minutes (3:43 - 10:55)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Vectors (beginning of V3)

#### 1D Kinematics Problem

RealVideo®
10:14 minutes (10:55 - 21:09)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Kinematics (beginning of V2)

#### Velocity in Kinematics Problems

RealVideo®
5:33 minutes (21:09 - 26:42)

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

Instructor: Prof. Walter Lewin
Prior Knowledge: Kinematics (beginning of V2)

## Lecture Notes

#### Velocity

PDF - 1.3 MB#
Page 1 to page 5

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Derivatives

#### Acceleration

PDF - 1.5 MB#
Page 1 to page 3

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Lecture 2

#### Acceleration of Gravity

PDF - 1.5 MB#
Page 3 to page 6

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: Acceleration

#### One-Dimensional Kinematics

PDF
Page 1 to page 2

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

Instructor: Dr. George Stephans
Prior Knowledge: Derivatives

#### One-Dimensional Motion

PDF
Page 1 to page 11

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

Prior Knowledge: Vector notation, derivatives

#### Constant Acceleration

PDF
Page 12 to page 26

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.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: One Dimensional Motion, integrals

## Practice Problems

#### Dimensions of Displacement

PDF
Problem 2

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Half Time vs. Half Distance

PDF
Problem 3

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Acceleration Curves

PDF
Problem 4

Sketching velocity curves within displacement and acceleration parameters.

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Collision of Dropped Balls

PDF
Problem 5

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Kinematics in One-Dimension

PDF
Problem 1 to problem 2

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

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Car and Motorcycle

PDF
Problem 1

One dimensional motion of two vehicles.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Displacement

PDF
Problem 1

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

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Vertical Motion

PDF
Problem 2

Motion of a ball thrown vertically. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Position and Velocity

PDF
Problem 3

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

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Relative Velocity

PDF
Problem 4

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

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Relative Position

PDF
Problem 5

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

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Falling Stones

PDF
Problem 6

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

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Falling Balls

PDF
Problem 7

Velocities of two vertically thrown balls. Solution not included.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Kinematics

PDF
Problem 2

Relative motion of two falling stones.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### One-Dimensional Motion

PDF
Problem 4

Modelling the motion of a person catching a streetcar.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Measurement of g

PDF
Problem 1

Measuring the acceleration of gravity by timing a falling ball.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### One-Dimensional Kinematics: Track Event

PDF
Problem 2

Motion of two runners in a race.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### Relative Inertial Frames

PDF
Problem 1

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

Prior Knowledge: None

#### 1D Kinematics

PDF#
Problem 10

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

Instructor: Prof. Walter Lewin
Prior Knowledge: None

#### Plane Round-Trip

PDF#
Problem 16

Calculating travel time dependent and independent of wind.

Instructor: Prof. Walter Lewin
Prior Knowledge: None

## Exam Questions

#### 1D Kinematics

PDF#
Problem 1

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

Instructor: Prof. Stanley Kowalski
Prior Knowledge: None

#### Airplane Against Wind

PDF
Problem 1

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

Prior Knowledge: None

#### Motion in One-Dimension

PDF
Problem 1

Position, velocity, and acceleration of a runner.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Acceleration

PDF
Problem 4

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

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Slowing a Speeding Car

PDF
Problem 8

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

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Rocket Flight

PDF
Problem 9

Vertical motion of a rocket.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Jumping Man

PDF#
Problem 5

Motion of and forces acting on a jumping basketball player.

Instructor: Dr. George Stephans
Prior Knowledge: None

#### Space Shuttle

PDF
Problem CQ3

Average speed of a space shuttle during fuel consumption.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### One-Dimensional Kinematics: Track Event

PDF
Problem 1

Motion of two runners in a race.

Instructors: Dr. Peter Dourmashkin, Prof. J. David Litster, Prof. David Pritchard, Prof. Bernd Surrow
Prior Knowledge: None

#### 3D and 1D Kinematics

PDF#
Problem 2

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

Instructor: Prof. Walter Lewin
Prior Knowledge: None