A way to determine if a body accelerates or loses speed at a certain time With given vectors for acceleration and velocity, is there a way to determine if a body accelerates or decelerates at a certain time-interval? Can this be determined, for instance, by simply observing the vectors? 
 A: 
With given vectors for acceleration and velocity, is there a way to determine if a body accelerates or decelerates at a certain time-interval?

Given the velocity vectors of a (specific) body (with respect to specific members of a suitable reference system) throughout a trial, in particular the velocity vectors $\mathbf v_{\text{initial}}$ at the beginning of the trial and $\mathbf v_{\text{final}}$ at the end of the trial, then


*

*the body is said to have "gained speed" (on average, over the course of the trial) if $\| \mathbf v_{\text{final}} \| \gt \|  \mathbf v_{\text{initial}} \|$,
where the double bars denote the magnitude (norm) of the vector; and

*the body is said to have "lost speed" (on average, over the course of the trial) if $\| \mathbf v_{\text{final}} \| \lt \| \mathbf v_{\text{initial}} \|.$

Can this be determined, for instance, by simply observing the vectors? 

No, not merely "by observing". Instead, the magnitudes of vectors, in comparison to each other, are to be measured; i.e. derived from observational data, to obtain unambiguous commensurate values.
