Uploaded April 2026 | Updated September 2026, 3 weeks 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
Notes and playlists:
- 3Speak: 3speak.tv/watch?v=mes/e443f9d3
- Summary: inleo.io/threads/view/mes/re-leothreads-374plp6cw
- Hive Notes: peakd.com/hive-128780/@mes/e443f9d3
- PDF Notes: https://1drv.ms/b/c/88862ef47bcaf6cd/IQDQ6cRoDbwpQIVaxkNMuZ_uAeUUOamXdKOXCFLp_yhOZQs
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0Hxo8aPU3ezG0tcLvgJnxLB .
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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
Notes and playlists:
- 3Speak: 3speak.tv/watch?v=mes/e443f9d3
- Summary: inleo.io/threads/view/mes/re-leothreads-374plp6cw
- Hive Notes: peakd.com/hive-128780/@mes/e443f9d3
- PDF Notes: https://1drv.ms/b/c/88862ef47bcaf6cd/IQDQ6cRoDbwpQIVaxkNMuZ_uAeUUOamXdKOXCFLp_yhOZQs
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0Hxo8aPU3ezG0tcLvgJnxLB .
------------------------------------------------------
Become a MES Super Fan! youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: peakd.com/@mes
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
