Lesson 2.3 • Competency 2.1Complete Lesson
Back to UnitUniformly Accelerated Motion
Equations of linear motion under constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t, and free vertical fall under gravity.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Derive and apply the four kinematic equations for constant acceleration with directional sign discipline.
- Analyze vertical motion under gravity and calculate apex height, apex time, and impact velocity.
Core Theory & Concepts
When a body experiences a constant net force, it undergoes uniform acceleration. Its velocity changes at a steady rate, governed by four canonical kinematic equations.
The Four Kinematic Equations
1. v = u + at 2. s = ut + ½at² 3. v² = u² + 2as 4. s = ½(u + v)t
v = u + at, s = ut + ½at², v² = u² + 2as
Vertical Motion Under Gravity
Taking upward direction as positive: a = -g. At the peak apex of flight, instantaneous vertical velocity v = 0.
v² = u² - 2gh (at apex: h_max = u² / 2g)
Common Misconceptions
Misconception
Believing acceleration is zero at the highest point of a vertical throw.
Physical Clarification:At the apex, velocity is instantaneously zero (v = 0), but gravitational acceleration remains continuous and downward (a = -g). If acceleration were zero, the ball would remain suspended in mid-air!
Syllabus Topic Outline
- 1Definition of acceleration as a = dv/dt
- 2Derivations of the four kinematic equations
- 3Vertical motion under gravity (g = 9.8 m s⁻²)
- 4Graphical analysis: velocity-time area and slope