554 Physics: Unit 2: 1-D Kinematics

Kinematics is the study of motion, that is, the relationship between an object's position, time, and the rate at which those change. The simplest descriptions and predictions of motion are for objects that don't move at all or only move back and forth along one dimension.

By the end of this unit, a successful student will be able to:

1. Define displacement, position, distance (2-1), speed, velocity (2-2, 2-3) and acceleration (2-4) (MSTE: Phys 1.2)

2. Recognize the algebraic relationships between the above quantities when acceleration is constant and use them to solve one-dimensional problems (2) (MSTE: Phys 1.2)

3. Distinguish between vector quantities (velocity, acceleration) and scalar quantities (speed) (2-1, 2-2) (MSTE: Phys 1.1)

4. Recognize the gravitational field strength near the Earth’s surface as being constant and resulting in a constant acceleration of 9.8 m/s². (2-7)

5. Create and interpret graphs of motion (position vs. time, speed vs. time, velocity vs. time, acceleration vs. time) including recognizing the role that slope and area under the function play in those interpretations. (2-8) (MSTE: Phys 1.3)

Note: Due to the limited number of in class hours, you may be expected to watch pre-recorded videos of lectures on topics we did not have time to adequately introduce during our direct interaction time.

Please check the course Google Classroom page daily for updates and relevant links.

All assignments are due on the date listed. That is not the date they are assigned.

Due date Day Assignment

9/16 Wed Introduction

9/17 Thu Read: 2-1 --> 2-6 (Goals 1, 2, 3)

Ungraded Practice: Questions (p 38): 1,2, 4, 5, 6, 8, 9, 10

Graded Practice: Questions (p. 38): 3, 7 ((Problem Set 1) (PS1)

9/18 Fri Ungraded Practice: Problems (p. 39): 2, 6, 7, 11, 14

Graded Practice: Problems: 7, 10 (PS 2) (Goals 1, 2, 3)

9/21 Mon A section in class goal: Collect data for lab

9/22 Tue Ungraded Practice: Problems: 19, 21, 27, 30, 32

Graded Practice: Problems: 22, 26 (PS 3) (Goals 1, 2, 3)

B section in class goal: Collect data for lab

9/23 Wed Read: 2-7, 2-8 (Goals 1 --> 5)

Ungraded Practice: Questions: 11 – 14; 16; 18 – 20

Graded Practice: Questions: 15, 17 (PS 4)

9/25 Fri Ungraded Practice: 37, 39, 47, 50, 52, 55, 58

Graded Practice: 42, 63 (PS 5) (Goals 1->5)

9/30 Wed Write: Acceleration lab

10/1 Thu Ungraded Practice: 69, 73, 75, 77, 82

Graded Practice: 64, 68 (PS 6) (Goals 1 --> 5)

10/2 Fri Test: Unit 2

Links - 1-D Kinematics

Missed a class? Forgot what we did last week? Follow the link to Physics Unit 2 Daily Plans

Classical Mechanics is the branch of physics first codified by Isaac Newton, built on a foundation laid by Galileo. It works out quite well so long as the velocities involved are much less than the speed of light in a vacuum, when relativity kicks in, or if you try to specify the momentum and position or energy and time of an object so closely that quantum uncertainty becomes important. Most everyday situations involving forces, mass, and energy, can be adequately described using classical mechanics.

• Prentice Hall's web page on Giancoli Chapter 2 Motion in 1-D
• Haliday, Resnick and Walker's page on Chapter 2 - Motion along a straight line (Calculus based)
• In addition to his astronomical discoveries and his popularization of the telescope as an astronomical instrument, Galileo Galilei (1564-1642) is credited with uncovering the law of inertia as well as recognizing that near the surface of the Earth all bodies fall at the same rate of acceleration. In addition, he recognized that an object's velocity is dependent upon the frame of reference of the observer, and that the motion of an object could be described separately in vertical, and two horizontal dimensions, thus developing the concept of Galilean relativity. Rice University's Galileo Project details much of his history.

Videos

• Motion In One Dimension (1-D Kinematics): Part 1: Position, Time, Displacement, and Velocity In this video we take a look at what we need in order to describe and quantify motion. We determine that at a minimum, we need position, which requires a frame of reference with a fixed origin and orientation, and time, also with a moment considered to be zero for time. We attempt to define position, time, and frames of reference. We also define displacement as the difference between positions at different times and develop notation to represent them. We use use data of two people walking at different rates of position with respect to time, plot that on a graph, and use that to motivate a definition for both instantaneous velocity and average velocity. We connect those quantities to slope on a position versus time graph.
• Motion in One Dimension (1-D Kinematics): Part 2: Scalars and Vectors After a brief recap of the previous lesson we define what scalar quantities and what vector quantities are and give some examples. In the process we differentiate speed from velocity and distance from displacement.
• Introduction to Vectors and Scalars Sal Khan defines vectors and scalars using distance, displacement, speed, and velocity as examples. Note: he uses an equation for speed which is more properly "average speed" not instantaneous speed. It is also redundant to say "The magnitude of speed".
• Calculating average velocity or speed. Sal Khan defines average velocity and solves a problem involving average velocity, distance and time. He also does a km/h to m/s unit conversion. Note: He uses the term "rate" as a synonym for speed. "Rate" is too vague. Speed is specifically the magnitude of the rate of change of position with respect to time. Also: Dimensional analysis is related to but is not the same as unit conversions.
• Solving for time Sal Khan solves a simple, constant velocity problem for time given the velocity and displacement. First he does so in a scalar variation of the problem. Note: "rate" is too vague and should not be used to mean speed (see above). Note2: Khan claims that delta is implied in writing "t". What this means is he is letting t = t-final, and 0 = t-original. He's being a little sloppy/informal in omitting the deltas here and for displacement.
• Displacement from time and velocity example Sal Khan works an example problem where constant velocity and time are given, and solves for displacement. His solution also involves a unit conversion.
• Motion In One Dimension (1-D Kinematics) Part 3: Changing Velocity and Displacement In this lecture, after a brief recap of previous principles we deduce the connection between displacement and a velocity versus time graph. We do this through a brief problem solving example and demonstrate some basic problem solving techniques. We draw the conclusion that the area under a velocity versus time curve is equal to the displacement over that time period.
• Frames of Reference: PSSC Physics Frames of reference, Galilean Relativity, Projectiles in constant v frames; Projectiles in constant a frames; accelerating frames and inertial frames; fictitious forces.
• Motion In One Dimension (1-D Kinematics) Part 4: Acceleration We define acceleration as the rate of change of velocity with respect to time and connect that to the slope of a velocity versus time curve. We use that and our previously deduced relationship between the area under velocity versus time curves and displacement, to determine equations showing the relationships between displacement, time, initial velocity, final velocity, and acceleration under conditions of constant acceleration.
• Motion In One Dimension (1-D Kinematics) Part 5: Constant Acceleration Problem Solving In this lecture we discuss general problem solving techniques that can be applied through out physics and other areas involving mathematical analysis. We apply that to an example problem involving a car slowing down to a stop under constant acceleration.
• Motion In One Dimension (1-D Kinematics) Part 6: Free Fall (Including Problem Solving) In this lecture we define free fall, describe how near the surface of the Earth that involves a constant acceleration downward at a rate of g, and use that to help solve an example problem.
• Demonstrating that in the absence of other forces (such as air resistance), astronaut David Scott shows that all objects fall at the same constant rate of acceleration by simultaneously dropping a hammer and feather on the Moon
• A video in which I demonstrate how objects near the surface of the Earth accelerate at the same rate, except when air resistance is significant. Siren: The constant acceleration of gravity near Earth's surface.
• Motion In One Dimension (1-D Kinematics) Part 7: Maximum Height In this lecture we look at what happens when an object is in freefall, launched upwards with some initial speed. We look at the symmetries of the speeds and heights with respect to time and each other. We take our existing equations of motion and derive an additional equation relating speeds to acceleration and displacement. We discuss what quantities have what values when an object reaches its maximum height. We use those relationships for approaching two problems involving high jumpers, both on Earth and on Mars.
• Motion In One Dimension (1-D Kinematics) Part 8: Rocket History and Two Accelerations After a brief overview of the history of rocketry from Chinese fire arrows to the beginnings of the Space Race we set up a problem determining the maximum speed and maximum height of a Mercury capsule if it had been launched completely vertically from a Redstone rocket. It has one average acceleration during the first part of flight, and is in free fall for the remainder of flight. (The real capsule experienced enormous air resistance on the way down).
• CalTech's freshman lecture on The Law of Falling Bodies from episode 2 of The Mechanical Universe. This lecture uses calculus, however an understanding of calculus is not required to follow the key ideas in this episode.
• Motion In One Dimension (1-D Kinematics) Extra: Using Calculus with Kinematics The integral and differential relationships between position, velocity, acceleration, and time are explored. The algebraic equations connecting those quantities for the case of constant acceleration are derived through integration. The term mathematical operator is defined and applied to derivative operators.

Kinematics Applets

• Average speed applet and sample problem by Andrew Duffy at B.U.
• Graphing constant velocity and constant acceleration motion applet position vs. time and velocity vs. time by Andrew Duffy at B.U.
• Graphing simultaneous position vs. time and velocity vs. time plots for constant velocity applet by Andrew Duffy at B.U.
• Problem with two cars, one accelerating and passing applet by Andrew Duffy at B.U.
• Plotting position vs. time, velocity vs. time, and acceleration vs. time for the above car problem
• Freefall problem applet by Andrew Duffy
• Freefall illustrating vector quantities (velocity, position, acceleration), applet by Andrew Duffy.
• Relative motion for constant velocities, applet by Andrew Duffy.
• A relative motion problem applet by Andrew Duffy.

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For more on kinematics you may be interested in:

The Cartoon Guide to Physics by Larry Gonick and Art Huffman