Instantaneous Velocity Explained: Why Derivatives Measure Speed at a Moment

Описание: 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

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📖 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.

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