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This lesson delves into the fundamentals of kinematics, focusing on displacement-time and velocity-time graphs. Students will learn how to interpret gradients representing velocity and acceleration, as well as the significance of the area under the graph for determining displacement. Key concepts include uniform vs non-uniform acceleration, and the distinction between instantaneous and average speeds. The session concludes with an exit quiz and an assignment to reinforce learning, ensuring students comprehend the applications of these kinematic principles in real-life scenarios.
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Kinematics (Part 2) Textbook Chp 2, Pg 27-38
Math Lesson! Calculus for Kinematics
Kinematics Graphs • Displacement-Time Graph • Gradient → Velocity • Velocity-Time Graph • Gradient → Acceleration • Area under graph → Displacement • Note: “area under graph” below horizontal axis is negative displacement!
Uniform & Non-Uniform Acceleration • Definition: Uniform acceleration is a constant rate of velocity • E.g. Freefall, ignoring air resistance • You are required to interpret and describe situations where acceleration is uniform as well as non-uniform (i.e. non-constant acceleration)
Instantaneous Speed / Velocity / Acceleration • Instantaneous speed / velocity / acceleration refers to the velocity / acceleration at a single instant in time. • Instantaneous speed / velocity is often contrasted against average speed / velocity. • In a kinematics graph, this refers to a single point on the graph. • E.g. Po and Shifu falling. Even though their velocity changes over time (because they are accelerating), at any one time, their instantaneous velocity are always equal to each other.
Summary • Distance vs Displacement • Speed vs Velocity • Average Speed vs Average Velocity • Acceleration • Free Fall (ignoring air resistance) • Displacement-Time Graph • Gradient → Velocity • Velocity-Time Graph • Gradient → Acceleration • Area under Graph → Displacement • Uniform & Non-Uniform Acceleration • Instantaneous Speed / Velocity / Acceleration • Reading & Describing of Graphs
Assignment • Due Wed 10 Apr **IN CLASS** • Textbook: Pg 47-48 • Section A Q1-4 • Section B Q2-4 • Estimated time to complete: 45 min • Do on Foolscap Paper