Parametric Equations are so Useful for Kinematics!!

Parametric equations x=f(t), y=g(t) can describe and understand the physical motion of a particle in the xy-plane (Kinematics in Physics). We can plot points to describe the curve, and we can use a graphing calculator. Derivatives from Calculus help us analyze the motion by finding velocity vectors and the speed as functions of time t, as well as the slope of the curve. Eliminating the parameter is sometimes important, including for uniform rectilinear motion along a line, uniform circular motion (constant speed), and motion along an ellipse. Sinusoidal functions are natural to use as well because of their periodic nature. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

Calculus and Physics Problems and Solutions

🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2): https://www.youtube.com/watch?v=lmCjnxzIals

🔴 Calculus 1, Lesson 1.2: Exponential Functions: https://www.youtube.com/watch?v=47ZqW19AjD4

🔴 Calculus 1, Lesson 1.3: Quadratic Functions, Transformations of Functions, and Function Composition: https://www.youtube.com/watch?v=1T58CnSME4g

🔴 Calculus 1, Lesson 1.4: Logarithmic Functions (Intro to Horizontal Compressions & Inverse Functions): https://www.youtube.com/watch?v=oS-gvIoJf60

🔴 Calculus 1, Lesson 1.5: Trigonometric Functions and Inverse Trigonometric Functions: https://www.youtube.com/watch?v=UFYjlnGUenE

🔴 AP Calculus AB Exam Review: Practice Exam Problems & Solutions (Multiple Choice, No Calculator): https://www.youtube.com/watch?v=2AG_Dt3x7q0

🔴 AP Calculus AB Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=RLgUwP44V_M

🔴 AP Calculus BC Exam Review: Practice Exam (30 Question Multiple Choice, No Calculator): https://www.youtube.com/watch?v=1Q7ALcwT97A

🔴 AP Calculus BC Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=ZWisJEDP44w

🔴 Calculus 1 Exam 1 Review Problems and Solutions (Precalculus, Limits, Continuity, Derivatives): https://www.youtube.com/watch?v=UjmvUwvd7c4

🔴 Calculus 1 Course, Lecture 1: The Big Ideas (Rates & Areas, the Infinity Principle & Circular Area): https://www.youtube.com/watch?v=2V_ehJC5QUY

🔴 Calculus 1 Course Lecture Playlist: https://www.youtube.com/playlist?list=PLmU0FIlJY-MkFrKtM0S0NLu-TxZa5jBIx

#ParametricEquations #ParametricCurves #calculus

Links and resources
===============================
🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinneymath?sub_confirmation=1
🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/
🔴 Follow me on Twitter: https://twitter.com/billkinneymath
🔴 Follow me on Instagram: https://www.instagram.com/billkinneymath/
🔴 You can support me by buying “Infinite Powers, How Calculus Reveals the Secrets of the Universe”, by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA.
🔴 Check out my artist son Tyler Kinney’s website: https://www.tylertkinney.co/

(0:00) Graph a piecewise linear parametric curve (the component functions are piecewise linear)
(8:08) Graph x = t^3 – 3t, y = t^2 (parametric equations)
(15:12) Velocity vector
(21:58) Speed of motion. Is it ever zero?
(25:55) Tangent lines: Where horizontal? Where vertical?
(33:42) Parametric equations for a circle. Describe motion.
(48:07) Parametrize a line segment
(51:43) Eliminate the parameter to get the xy-equation for the curve of motion
(54:12) Parameterize an ellipse

AMAZON ASSOCIATE
As an Amazon Associate I earn from qualifying purchases.