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Lecture 1: One-Dimensional Kinematics
August 26, 2025
Reading Assignment
- Read: 2-1, 2-2, 2-3
- Study: Ex 2.1; Figs 2.4, 2.5; Got It 2.2; Ex 2.2; Fig 2.7
Objectives
- (Continuing objective) Relate concepts of classical mechanics to “everyday” situations and discuss various applications of the concepts to practical problems in various fields of science, medicine and engineering.
- (Lab objective) Know how to determine the uncertainty in a calculated quantity due to the uncertainty in a measurement; how to combine uncertainties due to independent measurements; how to report results with the correct number of significant figures and units. Understand how to interpret uncertainties when comparing two experimental results or when comparing an experimental result to a theoretical prediction.
- Know the definitions of displacement, instantaneous velocity, instantaneous speed, and instantaneous acceleration. Use these concepts in problems involving moving objects.
- Use graphical methods to relate graphs of position, velocity, and acceleration for one-dimensional motion.
Homework
- Wednesday's Assigned Problems: A1, A5, A6; CH 2 #6, 19, 101, 102
Answers: CH 2 #101 answer should be choice c, which corresponds to point D on the graph. CH 2 #102 answer is b, which corresponds to point E on the graph. - Monday's Hand-In Problems related to today's lecture: A2, A4, A90; CH 2 #18abc, 52
Lecture Materials
Videos of example problems
Click the link, read the problem statement at the top of the page, and then scroll down for the embedded video.- Example of using derivatives to calculate velocity and acceleration in 1D
- Example of drawing graphs for 1D motion.
- Determining displacement from a velocity vs. time graphs for simple case where you can do areas of rec tangles and triangles.
- Determining displacement from a velocity vs. time graphs where you have to estimate the area under the curve. ans: 16 m
Pre-Class Entertainment
Guide to assigned problems
- A1: This is the most interesting and most challenging question of the entire set. Give it a try, but most of you will have significant difficulty with this and we will certainly be talking about this in problem session. (Here is an example where the first question in the set ends up being the most challenging.) Also, you will get the toys in problem session, so maybe wait until then to try the problem.
- A5: Similar to A1, this one is also very interesting but quite challenging. Again, you'll get the toys in problem session, so maybe wait until then.
- A6: This is basically practice with taking derivatives. If you have not seen this before, you should go to the optional calculus review session Tuesday evening.
- 2-6: This is an important conceptual question. It won't take long to try to answer this, but if you aren't confident in your answer, feel free to ask during problem session or office hours.
- 2-19: Slightly more challenging calculus (derivatives) problem.
- 2-101: Figuring out relative speeds by looking at slopes of curves. NOTE: Some of the books have an answer in the back that isn't correct.
- 2-102: Interpreting graphs by looking at area under curve.