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The area under the acceleration-time graph gives:
A.) Distance travelled
B.) Change in direction
C.) Force acting
D.) Change in velocity

Answer
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Hint: Try to understand the concept of graphs between two physical quantities. Draw an acceleration-time graph. Try to find the area of the graph with the help of physical notations. Then we can find our answer.

Complete step by step answer:
An acceleration-time graph is represented as the acceleration on the y-axis or the vertical axis and time in the x-axis or the horizontal axis. The value of the graph at a particular time will give us the acceleration of the object at that point of time.

Slope of an acceleration-time graph is known as a jerk. It gives us the rate of change of acceleration.

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We can find the area under the acceleration-time graph for a certain time interval.

Area under the graph can be defined as, area =Δa×Δt

Where, Δt is the time interval and Δa the change in acceleration in that time interval.

Now we can find acceleration as,

Δa=ΔvΔt

So, by multiplying both sides of equation by Δt , we can write,

Δa×Δt=Δv

So, the area under the acceleration-time graph can be given as,

area =Δa×Δt=Δv

Which is the rate of change of velocity.

So, the area under any acceleration time graph at a certain time interval will give us the rate of change of velocity.

The correct option is (a).

Note: For a constant acceleration we will get a linear graph parallel to the time axis. If we have a uniformly increasing acceleration, we will get a straight line with a slope. For non-uniform acceleration we won’t get a straight-line graph.
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