Instantaneous Velocity Explained: Why Derivatives Measure Speed at a Moment скачать в хорошем качестве

Instantaneous Velocity Explained: Why Derivatives Measure Speed at a Moment

How can your speedometer show 65 mph when an instant has zero duration? This video resolves the paradox by showing how limits capture velocity at a single moment—connecting the geometric concept of tangent slopes to the physics of motion. You'll see the complete step-by-step algebra for finding instantaneous velocity, learn why factoring out H is the key trick, and discover how one general formula lets you find velocity at any time without repeating the limit process. 📚 Key concepts covered: • Why average velocity (secant slope) approaches instantaneous velocity (tangent slope) as intervals shrink • The limit definition of instantaneous velocity: lim(h→0) [s(t₀+h) - s(t₀)] / h • Full 9-step worked example finding velocity at t = 5 for s(t) = 500 - 16t² • Deriving the general velocity formula v(t) = -32t for falling objects • The difference between velocity (includes direction) and speed (magnitude only) • How slope, instantaneous velocity, and rate of change are the same mathematical operation ───────────────────────────── 📖 ORIGINAL SOURCE This video distills concepts from a longer lecture. Source:    • Calculus 1 Lecture 1.5:  Slope of a Curve,...   Full credit to the original creator for the educational content. ───────────────────────────── 📺 About Lecture Distilled Long lectures. Short videos. Core insights. We transform lengthy academic lectures into focused concept videos that respect your time while preserving the depth of understanding. Explore our resources: https://github.com/Augustinus12835/au... ───────────────────────────── #Calculus #Derivatives #InstantaneousVelocity #RateOfChange #Limits #MathEducation #Physics #TangentLine