Vector valued velocity and acceleration question

[leehufford]

Hello,

In my multivariable calc class we are differentiating and integrating position, velocity and acceleration vector valued functions. My question is this:

When we integrate a vector valued function from acceleration to position, the constant vector only changes the definition of the functions that were not zero for acceleration. For example if the position function is <1,0,0> and the acceleration function is <0,1,0> , you could never recover that initial x motion from integrating the acceleration function.

What am I missing here? I understand the constant from integration is in the form of a vector now but this doesn't help me see what's wrong. Thanks for reading,

Lee

 

[AdkinsJr]

This doesn't make sense because the position in the y component and z component are constant and 0, so there is no acceleration in this direction.

 

[xAxis]

Any Two integrals are equal up to a constant term. The fact that the constant after integrating acceleration is a vector (velocity) doesn't mean that that integral is "more determined". You cannot recover exact situation unless given more than just acceleration function.