Example 3: Integrating Acceleration and Velocity Vectors to get the Position Vector

In this video, I show that we can obtain the velocity of a moving object by first integrating its acceleration vector to obtain its velocity and then integrating the velocity vector. This follows from my earlier videos on derivatives and integrals of vector functions by their components. I illustrate this with an example and show that the integration constants can be solved by plugging in the initial time variable, in our case t = 0. Thus, the velocity vector is the initial velocity plus the definite integral of the acceleration, while the position vector is the initial position plus the definite integral of the velocity.

#math #vectors #calculus #physics #Geogebra