Can you have two different velocities at the same time?

Question

Δt=0 {change in time is 0
v_f≠v_i {there are two different velocities (final velocity does not equal initial velocity)

What I'm saying is this: if no time has passed, can your final and initial velocities be the same?

The exact question is phrased like this: Is it possible to have Δt=0 and v_f≠v_i? Why or why not?

I'm just kind of lost right now. And by kind of I mean a lot.

Thanks a bunch!!

Answer 1

v = v(t)

 

v1 = v(t1)

 

v2 = v(t2)

 

If t1 = t2 (i.e. if Δt = 0) then v1 = v2.

 

So if no time has passed, the velocity is unchanged.  At the same instant t, the velocity must be unique, otherwise it would not be a function of t in the sense that functions are defined.  

 

However, the velocity is always relative to some reference frame.  At one instant, the same body can have different velocities relative to say a fixed frame and a moving frame, or relative to two frames moving at different velocities.  That might have been the context of the question.  Is more information stated in the original question?