Uploaded April 2026 | Updated September 2026, 3 weeks ago
In this video, I go over an example of obtaining and graphing the velocity and acceleration vectors of an object moving in 3D whose position vector is known. This follows from my earlier video in which I showed that the velocity of an object is just the derivative of its position vector, and likewise, the acceleration is the derivative of the velocity vector — hence the second derivative of the position vector. The speed of the moving object is obtained just by the magnitude or length of the velocity vector, which we can calculate using the distance formula in 3 dimensions. I also plot this out in the amazing GeoGebra 3D graphing calculator, which you can play around with here: geogebra.org/3d/h7epqemu
#math #vectors #calculus #physics #Geogebra
Timestamps:
- Example 3: Object moving in 3D – 0:00
- Solution: Velocity is the first derivative of position, and acceleration is the second derivative – 0:21
- Speed is the magnitude of the velocity vector – 2:47
- Graphing the velocity and acceleration vectors at t = 1 – 3:56
- Inputs for GeoGebra 3D graphing calculator – 9:50
- Graphing in GeoGebra – 12:00
Notes and playlists:
- 3Speak: 3speak.tv/watch?v=mes/e8759ef8
- Summary: inleo.io/threads/view/mes/re-leothreads-2eess8dpa
- Hive Notes: peakd.com/hive-128780/@mes/e443f9d3
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0Hxo8aPU3ezG0tcLvgJnxLB .
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In this video, I go over an example of obtaining and graphing the velocity and acceleration vectors of an object moving in 3D whose position vector is known. This follows from my earlier video in which I showed that the velocity of an object is just the derivative of its position vector, and likewise, the acceleration is the derivative of the velocity vector — hence the second derivative of the position vector. The speed of the moving object is obtained just by the magnitude or length of the velocity vector, which we can calculate using the distance formula in 3 dimensions. I also plot this out in the amazing GeoGebra 3D graphing calculator, which you can play around with here: geogebra.org/3d/h7epqemu
#math #vectors #calculus #physics #Geogebra
Timestamps:
- Example 3: Object moving in 3D – 0:00
- Solution: Velocity is the first derivative of position, and acceleration is the second derivative – 0:21
- Speed is the magnitude of the velocity vector – 2:47
- Graphing the velocity and acceleration vectors at t = 1 – 3:56
- Inputs for GeoGebra 3D graphing calculator – 9:50
- Graphing in GeoGebra – 12:00
Notes and playlists:
- 3Speak: 3speak.tv/watch?v=mes/e8759ef8
- Summary: inleo.io/threads/view/mes/re-leothreads-2eess8dpa
- Hive Notes: peakd.com/hive-128780/@mes/e443f9d3
- 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
