Acceleration/Velocity Relationship

[tascja]

i was wondering if someone could explain the relationship between distance/velocity/acceleration? I don't have a clear understanding how they are related.. especially when they are plotted on a graph.

Ill give you a specific example:
so there was a velocity-time graph where the average acceleration (slope) over the entire graph was 0.5m/s^2. The instantaneous acceleration at t=16s was -1m/s^2. And it asked if the average acceleration was greater than the instantaneous or was the instantaneous greater than the average?
My thoughts were that since the instantaneous acceleration was greater in magnitude it was greater... this was wrong :( but i don't understand how or why??

 

[LowlyPion]

Velocity is the Δd/Δt. It is the time rate of change of displacement.

Acceleration the is the Δv/Δt = Δ (Δd/Δt) /Δt or Δ²d/Δt²

Both of these are vectors - and direction matters just like the displacement vector d that they are expressions of. You should view them as a continuum.

Hence -1 is greater than -2 but less than .5.