Motion in Space: Velocity and Acceleration

in DTube • 2 days ago

In this video, I go over further into vector functions, and this time look at motion in space in terms of the velocity, acceleration, and position of objects moving in 2D or 3D space. Using the fact that the rate of change of the position of an object is the velocity, and likewise that the rate of change of velocity is the acceleration, I show we can write the velocity and acceleration of an object just in terms of the derivatives of the position vector. Likewise, going backwards via vector integrals, we can obtain the velocity from the acceleration vector, and the position from the velocity vector. I also do an example on centripetal force, which is derived from Isaac Newton's 2nd law of motion, F = m⋅a, and arises for circular motion. In a future video, I will show how these equations are used in the famous Kepler's Laws of planetary motion!

#math #vectors #calculus #space #physics

Timestamps:

  • Intro – 0:00
  • Calculus Book reference – 1:00
  • Calculus book chapter – 1:25
  • Topics to cover – 2:29
  • Motion in Space: Velocity and Acceleration – 3:25
    • Example 1: Moving Particle in 2D – 14:37
    • Example 2: Moving Particle in 3D – 27:16
  • Integrating Acceleration and Velocity Vectors – 41:29
    • Example 3: Integrating to get Velocity and Position Vectors – 43:10
    • Summary: Vector Integrals to Recover Velocity and Position – 1:00:30
  • Isaac Newton's Second Law of Motion – 1:02:19
    • Example 4: Centripetal Force – 1:03:09
    • Example 5: Horizontal Distance of Projectile – 1:20:23
    • Example 6: Impact Speed of Projectile – 1:43:33
  • Tangential and Normal Components of Acceleration – 2:07:03
    • Acceleration Vector in terms of Derivatives of the Position Vector – 2:25:03
    • Example 7: Tangential and Normal Components of Acceleration – 2:44:00
  • Outro – 2:55:27

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2 days ago in DTube by
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