What Does the Area Under an Acceleration-Time Graph Indicate?

[roam]

Homework Statement

(a) What does the area under the acceleration-time graph represent? (Hint: it is NOT velocity or speed).

(b) What is a particle doing when the graph is above or below the axis? (Hint: a graph below the axis does NOT necessarily mean deceleration).

The Attempt at a Solution

Can someone explain these two for me, I am very confused.

 

[rl.bhat]

The area under the acceleration-time graph = a*Δt = ...?

 

[roam]

The area under the acceleration-time graph = a*Δt = ...?

v? but the questions says "it is NOT velocity or speed"!

 

[faradayslaw]

The area under the acceleration time graph along a given time interval is the change in velocity along that interval, and a negative acceleration means that the particle's velocity becomes more negative. Negative acceleration may not necessarily be deceleration, since the particle's velocity could be in the negative direction itself, thus a negative acceleration speeds up the particle! A positive acceleration just means that the particle's velocity becomes more positive with respect to time