Calculate the gradient of the curve which will give the acceleration. Change the sign of the answer to convert acceleration into retardation.
In statistics you can find the area under a curve to establish what to expect between two input numbers. If there is a lot of area under the curve the graph is tall and there is a higher probability of things occurring there than when the graph is low.
The distance from the origin at time t, in the direction of motion, is the area under the graph between time 0 and time t. In a simple speed-time graph the area may be calculated using simple formulae for the areas of triangles, rectangles, trapeziums. In more complicated cases you will need to integrate for the area under the speed-time curve. And in seriously complex cases, you will have to use numerical estimation for the area.
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Assuming it's a graph of speed vs time, then between 2 times, the average is the distance (= area under the graph between those times) divided by the time difference.
It is the gradient (slope) of the line.
You find the point(s) at which the slope of the curve is greatest.
You find the slope of the tangent to the curve at the point of interest.
One word answer: integrate. The area under the acceleration curve, up to time T, is the speed at time T. If you now make a curve of the speed as a function of time, and find the area under that up to time T, that will be the position at time T.
In statistics you can find the area under a curve to establish what to expect between two input numbers. If there is a lot of area under the curve the graph is tall and there is a higher probability of things occurring there than when the graph is low.
Acceleration=change in y graph/change in x graph
No. What you've described is instantaneous acceleration. To lift the average speed from a graph, you need a graph of distance-time. Pick two points in time, and find the distance at both those times. The average speed over that time interval is (difference between the distances at the beginning and end) divided by (difference between the two times). If you're just going for the average, then it doesn't matter what happened during the interval, only the values at the end-points. The slope of the line tangent to the curve on your distance-time graph is the instantaneous speed at that point in time. We're saying "speed" in this discussion because there's actually no such thing as a graph of velocity. No simple thing anyway. Velocity is a vector, whose magnitude is speed and which includes a direction. It's easy to graph speed vs time, but not that easy to graph direction vs time. So all the graph shows is speed.
Reteradation will be half of acceleration
You can't, since the slope of the graph means average velocity and the area of the graph has no meaning. The only way to find instantaneous velocity from position-time gragh is by plugging the data into the kinematic equations to get the answer. Edit: Actually you can if you take the derivative of the equation of the curve it will give you the equation of the velocity curve
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The distance from the origin at time t, in the direction of motion, is the area under the graph between time 0 and time t. In a simple speed-time graph the area may be calculated using simple formulae for the areas of triangles, rectangles, trapeziums. In more complicated cases you will need to integrate for the area under the speed-time curve. And in seriously complex cases, you will have to use numerical estimation for the area.
Assuming it's a graph of speed vs time, then between 2 times, the average is the distance (= area under the graph between those times) divided by the time difference.
It is the gradient (slope) of the line.