**Unit 1: Motion in One Dimension**

**Unit 1: Motion in One Dimension**

BJU book: Read Ch. 3 "Motion in one dimension"

AP students additional reading: Princeton Review Ch. 4 "Kinematics". You can skip the part on "Projectile Motion", as we will cover that topic later.

__Reading__BJU book: Read Ch. 3 "Motion in one dimension"

AP students additional reading: Princeton Review Ch. 4 "Kinematics". You can skip the part on "Projectile Motion", as we will cover that topic later.

__Topics__- Displacement, speed, velocity, and acceleration
- The "Big Five" equations of motion

__Labs__- 2021-2022: Skate Park Velocity-Acceleration Weblab

__Lecture outline:__

Velocity

- Velocity indicates how your location changes with time. It is distance divided by time, as in “miles per hour” or “meters per second”
- We write the formula as follows:

vavg = (x2 – x1) / (t2 – t1)

Acceleration

- Acceleration indicates how your
__velocity__changes with time. - Positive acceleration means "speeding up". Negative acceleration (i.e. deceleration) means "slowing down".
- We use units of "meters per second per second" or "meters per second squared".
- We write the formula as follows

aavg = (v2 – v1) / (t2 – t1)

The five (5) equations of motion: "The Big Five"

- You will use these 5 equations for the
__next several chapters__! Locate them in your book and mark the page; you will be referring to them over and over again.

__Lecture video__

__2021-2022 Class: Skate Park Velocity-Acceleration Weblab, part 1__

Follow the instructions in the handout below. Upload your completed work to Canvas by the due date.

Online Curve Fitting Calculator: elsenaju.eu/Calculator/online-curve-fit.htm

skate_park_velocity-acceleration_weblab, part 1.docx |

__2020-21 Class: Galileo's Inclined Plane experiment__

Cart-track velocity lab using tracker video analysis https://www.compadre.org/osp/items/detail.cfm?ID=7365.

- In this lab exercise we reproduce Galileo's famous inclined-plane experiment using a modern Vernier cart and track set at 3 different angles.
- This is exactly what Galileo did using a bronze ball and wooden track with a groove down the middle. Galileo, however, didn't have a movie camera with an electronic timer; his "clock" was allowing water to drip into a container and then weighing the container!
- Our goal is to estimate 'g', the acceleration due to gravity on planet Earth, and compare with the known value of 9.8 m/sec^2.

__Galileo Lab, part 1__

- Elevate one end of the track at 3 different heights, such that you have a 'slow', 'medium', and 'fast' cart moving down the track.
- Using a movie camera (or motion app) and cart, record "distance vs. time" down the 2-meter track for each scenario: 1) slow, 2) medium, 3) fast. Record the raw data in the form of a table. See example below.
- Create a "distance-vs-time plot" of the raw data we gathered. You will have 3 curves, one for each ramp angle we used. See example below.
- Label everything and make it look nice & professional. Use circles, squares, and triangles as shown. Sketch nice-looking best-fit curves. TAKE PRIDE IN YOUR WORK.

__Galileo Lab, part 2__

- Compute the final velocity of the cart for each track-scenario: Do this by carefully drawing a tangent line (at a convenient spot
__near the top__of each curve), constructing a triangle, and calculating the slope of the curve at that point. Recall that slope is equal to (y2-y1)/(x2-x1), which is the same as "rise-over-run". If you draw your triangle carefully, you can fairly-easily count-out (y2-y1)/(x2-x1) on your graph paper, which will give you the slope at that point, which is equivalent to 'velocity' in m/s. Again, recall that when you plot "distance-vs-time", with distance on the Y-axis, the slope of the curve at any point is equal to 'velocity'. The velocity you are calculating is the 'final velocity' of the cart - or at least the final velocity at the 'time' you draw your tangent line at. See example below. - Use equation #5 of the Big Five (listed above) to compute the acceleration of the cart down each track: 1) slow track, 2) medium track, and 3) fast track.
- Using the principle of "similar triangles", calculate the acceleration of gravity 'g' for each of the 3 runs. See example below.
- Analysis: compare your 3 values of 'g' with the known value of 9.8 m/s^2. Compute the % error between your average value and the 'true' value of 9.8 m/s^2. Try to explain any differences.

galileo_lab__part_1_raw_data_table_example_.pdf |

galileo_lab__part_1_distance_vs_time_plots_examples_.pdf |

galileo_lab__part_2_final_report_example_.pdf |

Use this graph paper:

**http://www.printfreegraphpaper.com/gp/e-i-110.pdf**__Homework__

Velocity problems: BJU Ch. 3 Review Questions #20-27 and 38 (9 problems). Enter your answers in Canvas.

AP: Velocity problems posted in Canvas.

2._acceleration_homework_problems_2021.docx |