The mathematical technique used to calculate the area under a graph is integral calculus. This is a complex subject which I am not going to attempt to explain in detail- it normally takes years of study.
The area under an acceleration-time graph is equal to the object's velocity (not change in velocity).
It is not, if it is a graph of force against acceleration.
change in velocity
Displacement is the area under the v-t graph.
The distance travelled over the time period represented by the area under the v-t graph between the end points.
The area under an acceleration-time graph is equal to the object's velocity (not change in velocity).
It is not, if it is a graph of force against acceleration.
Velocity.
The physical quantity measured under a speed-time graph is acceleration. This is because acceleration is represented by the gradient of the graph, where a steeper gradient indicates a higher acceleration.
To determine velocity from an acceleration-time graph, you can find the area under the curve of the graph. This area represents the change in velocity over time. By calculating this area, you can determine the velocity at any given point on the graph.
To calculate the distance traveled from a velocity-time graph, you need to calculate the area under the graph. The number of calculations you need to make, and the shapes you divide the area into will depend on the shape of the curve.The skinnier you make the slices, and the more area measurements you make,the more accurate your answer will be.In the kind of math called "calculus", there's a way to work that problem as if thewidth of the slices was zero and there was an infinite number of them, so that the answer comes out exactly right. It's called "integration."
The area under the acceleration-time graph represents the change in velocity over a given time interval. It provides information about how the velocity of an object changes over time, with positive area indicating acceleration and negative area indicating deceleration.
From a velocity-time graph, you can calculate the acceleration by finding the slope of the graph at a certain point. The area under the graph represents the displacement of the object. You can also determine the direction of motion based on the slope of the graph (positive slope indicates motion in one direction, negative slope indicates motion in the opposite direction).
Since jerk is defined as the derivative (the rate of change) of acceleration, in the case of the area under the curve, it is the other way round: the integral (area under the curve) for jerk is the acceleration.
Nothing in particular. It certainly does not represent acceleration.
No, displacement is the area under the velocity vs. time graph. The slope of a velocity vs. time graph represents acceleration.
To find the position of an object from a velocity-time graph, you need to calculate the area under the curve of the graph. This area represents the displacement of the object.