What is Acceleration Time Graph?

An acceleration-time graph is used to depict the relationship between acceleration and time, where acceleration is an independent variable plotted on the Y-axis, and time is a dependent variable plotted on the X-axis. It is obtained when the data of acceleration and time obtained is plotted on a rectangular graph while studying the motion of a body. We can determine the change in velocity in a given interval of time with the help of an acceleration-time graph. By determining the area under the curve of the acceleration-time graph, we can find the change in velocity of an object in motion over a certain period. 

The graphs shown above are acceleration-time graphs for various types of body motion.

1. When a body is moving with constant acceleration, 
2. When a body is moving uniformly with increasing acceleration.
3. When a body is moving non-uniformly with variable acceleration.

Conclusions

The following are the points concluded from the acceleration-time graphs.

• The slope of the acceleration-time graph is △a/△t.
• The area under the acceleration-time graph represents the change in velocity. 

Let,

△v be the change in velocity, 

△a be the change in acceleration, 

△t be the change in time.

Now, the area under the curve = △v

We know that the acceleration of a body is referred to as the rate of the change in velocity in a given period of time.

So,

△a = △v/△t

Now, by multiplying with △t on both sides, we get,

△v = △a × △t      (which is area under the curve in acceleration-time graph)

• For an object moving with constant acceleration, i.e., acceleration is the same at all intervals of time. Hence, the slope of the acceleration-time graph is zero, and the graph will be parallel to the time axis.

Acceleration is the change of velocity with time. In real life scenario acceleration also changes with time. For example, you are travelling from one city to another city by road. Then in this case you will accelerate more in case of empty road and will accelerate down in case of traffic. This change of acceleration can be observed by plotting acceleration against time in a graph. This called acceleration time graph. In this article, we will learn in detail about acceleration time graph and solve problems based on it.