16) This question simply asks us which quantity we will find if we take the area under an acceleration versus time graph.
The area under the acceleration versus time graph is the integral of the curve.
Our goal is to solve this equation above.
It is commonly known that the slope of our velocity graph is the instantaneous acceleration, so we will start with this.
Next, we can use the separation of variables to integrate both sides of the equation.
If we compare what we currently have, to the goal we set at the beginning of the problem, you can see that the left side matches up. Let's leave the left side alone and solve the definite integral on the right side.
This final expression shows us that the area under an acceleration versus time curve is the change in velocity.
Answer: D
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