Example 2: Velocity and Acceleration of an Object moving in 3D

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: https://www.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 .

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