Whenever an object's velocity changes, the object is said to be accelerating. If the acceleration occurs while the object is moving in a straight line, then we say that the object is experiencing rectilinear acceleration. An example of this type of acceleration occurs whenever an automaker brags that his vehicle can go from 060 mph is "xnumber" of seconds. He is assuming that you understand that the car is merely gaining speed, not randomly changing speed in a number of different random directions.
When a velocitytime graph lies in the 1st quadrant, the object is traveling in a positive direction. If the line slopes away from the x or time axis, it is gaining speed; if it slopes towards the x or time axis, it is losing speed.



gaining speed + acceleration

losing speed  acceleration

constant speed 0 acceleration

If the velocitytime graph lies in the 4th quadrant, then the object is losing or gaining speed in a negative direction.



gaining speed  acceleration

losing speed + acceleration

constant speed 0 acceleration

Notice that graphically, the acceleration is calculated as the slope of each velocitytime graph. The graph's slope which equals Δy/ Δx can just as easily be expressed as Δv/Δt, or acceleration.
But be careful! Notice that a positive acceleration does NOT always mean that the object is gaining speed. You cannot forget that acceleration is a vector quantity that represents the change in velocity, another vector quantity. Since vectors have two attributes: magnitude and direction, you can use the rules for signed numbers to remember which combinations result in either a positive or a negative acceleration. gaining speed (+) in a positive (+) direction + acceleration
gaining speed (+) in a negative () direction  acceleration
losing speed () in a positive (+) direction  acceleration
losing speed () in a negative () direction + acceleration
The area bounded by the velocitygraph and the nearest x or time axis tells you the object's displacement during a specified time interval. As stated before, whenever the graph is in the 1st quadrant, the object is moving in a positive direction and its area represents a positive displacement. Conversely, whenever the graph is in the 4th quadrant, the object is moving in a negative direction and its area represents a negative displacement. During our study, these areas will either be rectangles, triangles, or a combination of triangles and rectangles. You will have the opportunity to practice calculating areas (or displacements) in the following problem.
Let's look at an example to test our understanding of these properties of velocitytime graphs. 