Is acceleration correlated with an instantaneous velocity?

yes, acceleration is the rate of change of velocity respect to time.

 

Yes, since instantaneous acceleration is dv/dt, so this instantaneous acceleration determines how instantaneous velocity changes in an infinitesmall amount of time. i.e. the instantaneous acceleration determines how the instantaneous velocity changes in the vicinity of that instance.

 

Only instantaneous acceleration relates to instantaneous velocity. An average acceleration correlates to the two velocities of a time interval. For example if we have the time interval from [tex]t_1[/tex] to [tex]t_2[/tex] then the average acceleration for this time interval is [tex]a_{avg}=\frac{v_2-v_1}{t_2-t_1}[/tex] where v2 and v1 the velocities at time t2 and t1.

But to find the instantaneous acceleration we need to know the instanteneous velocity v(t) for every t inside (t1,t2) and not just only the two velocities v2 and v1 at the edges of the time interval t2 and t1. If we know v(t) then the instantaneous acceleration is [tex]a(t)=\frac{dv(t)}{dt}[/tex].

 

So, at any instant, can the instantaneous velocity be defined, or is it changing? ()

 

Similarly for velocity, we need to know the instantaneous location for every t inside an interval. If you know a location without also knowing what its location is at +Δt and -Δt then you cannot determine its velocity, but if you require a small interval of time to work out how it is moving, then it is no longer 'instantaneous'?!

 

Can be defined and its value at any instant t is v(t)