Question about integrating w/ specific time

AI Thread Summary
Integrating the velocity function v(t) after determining a specific time t, such as t=2, yields the position vector at that time. The integral should be calculated from 0 to t to find the position at t=2, but if calculating from t to another time T, the limits should reflect that change. It is crucial to understand that integrating after calculating t may limit the generality of the result. The correct approach is to use the integral from T1 to T2 to determine the change in position over that interval. Ultimately, the integration limits depend on the specific time frame being analyzed.
Lenjaku
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When I integrate v(t) after I calculated the t, what do I get?
Let;s say t=2.
do I get the position vector in this 2s?
If so it means the integral goes from 0 to t? or I still need to calculate from 2 to t?

I could simply integrate v from 0 to t then place 2 in the position vector but I got an ex here integrating after calculating the t...I knew I must not integrate vector after calculating the t since it won't be general anymore...but still there is a use for this it seems...
 
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I figure out I need to calculate 2 to t...
 
\int_{t=T_1}^{T_2}v(t).dt is the change in position from time T1 to time T2.
 

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