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Acceleration vs Time Graphs

Acceleration is the rate at which the velocity changes with respect to time. It is measured in measured in m/s$^{2} in standard unit system. To obtain an acceleration vs time graph we plot acceleration on y axis and time on x axis.


There are three possible case that we arrive on:

1) Zero acceleration graph 

2) Constant acceleration graph

3) Positive or Negative acceleration graph

These types of graphs not only give information about acceleration but also about velocity of the object being talked about. For example if in some interval of time the acceleration is constant will not imply that the object is not accelerating, but it means that the velocity of the object is constant in that interval.

The slope of displacement time graph tells about the velocity of the object and the slope of the velocity time graph tells about the acceleration. The slope of an acceleration time graph does not symbolize any other variable unlike displacement time and velocity time graph. The slope of acceleration time graph simply tells about the rate of change of acceleration of the object with respect to time.

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Zero Acceleration Graph

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In this case, the acceleration is zero. This implies that the object or a person is moving with constant velocity that is the change in velocity is equal to zero. The zero acceleration graph is coincident to x axis that is the horizontal coordinate axis.

Constant Acceleration Graph

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A constant acceleration implies that the change in velocity of the object is constant or same at every instant. This means that the velocity of the object is increasing uniformly.
Constant Acceleration Graph
The picture shows constant acceleration graph. Here it is clear that the change in velocity is not equal to zero but a constant number at every instant of time.

Negative Acceleration (Deceleration) Graph

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Negative acceleration is also known as deceleration as acceleration is decreasing in this case.

This is the case of negative velocity that is the object is moving in the negative region of the graph. When the object moves in positive region that is above x axis of the graph then we always have positive velocity and hence a positive acceleration time graph as well. 
Negative Acceleration Graph
Deceleration can be constant or variable with which the shape of the graph varies. The pictures above show two graphs. The first one is a velocity time graph which is shown to understand the concept of deceleration better. One can clearly see the part of the graph where we have negative acceleration. Since the drop in acceleration is constant in this case so we call it constant deceleration.

In the second picture the first part of the graph showcases deceleration and then again negative acceleration is shown with changing direction as graph is crossing over the x axis. The third part of the graph displays constant acceleration and then again deceleration is displayed. The last part of the graph is an example of zero acceleration.

Steps & Methods

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Steps and methods based on solving Zero/Constant/Negative Acceleration

1)
We can determine area under the curve of the graph to find the velocity in different intervals. The intervals can be separated as the ones in     which acceleration is zero, in which the acceleration is constant and the ones with positive accelerative, the ones with deceleration.

2) We can also determine the change in velocity from the acceleration time curve, as when the curve coincides x axis, the change in velocity     of the object equals to zero since here then acceleration is equal to zero. When the graph is increasing straight up then we have positive         acceleration that is change in velocity of the object is positive. When the graph is falling down then we have deceleration that is change in       velocity in negative which implies the object is moving in negative region. When the graph is parallel to x coordinate axis this means that         the acceleration is a constant value which further implies that the change in velocity of the object is a constant number, that is, the object       is increasing its velocity at a constant rate.
At any point we should keep in mind the following things to solve problems based on acceleration of different types:

1) Analyse what kind of acceleration is given in the graph which should be properly done as this is the main step and also the first step.

2) Find the change in velocity accordingly as the type of acceleration been determined.

3) Then we can use the values from first and second steps anywhere as required in the given problem.
At all points it should be kept in mind that the acceleration is a vector quantity and not a scalar one and so the direction of the acceleration of the object is very important and so does that of velocity which is also a vector quantity.
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