Acceleration Time Graph

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By the use of acceleration time graph we can calculate acceleration at any specific time as well as velocity. The change in velocity in the given time will be the area under the graph with that time. It will be clearer with the help of the acceleration time graph.



In the above graph, from t = 2 to t = 5, the acceleration at 1 m/s^2 but from t = 6 to t = 7, the acceleration will be zero that means no acceleration so that the velocity is constant.

From time t = 2 to t = 5, acceleration is 1 m/s^2, so that the change in velocity will be the area of rectangle ABCD represented by the green rectangle box in the graph.

Therefore, Change in velocity = Area of rectangle ABCD
                                                      = 1 x (5 - 2) = 1 x 3 = 3 m/s.




Example1:  In the above acceleration-time graph. Find the velocity between time 2 sec to 4 sec.

Solution: In the graph, between 2 sec to 4 sec the shape will be rectangular.
We know that the area of the shape formed in the graph is velocity in acceleration-time graph.
So that the area of rectangle = 3 x (4-2) = 3 x 2 = 6 m/s
 
Example2: In the above acceleration-time graph. Find the velocity between time 4 sec to 6 sec.

Solution: In the graph, between 4 sec to 6 sec the shape will be triangular.
We know that the area of the shape formed in the graph is the velocity in acceleration-time graph.
So that the area of triangle = ½ (3)(2) = 3 m/s


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