Lets assume a function a = |sin t| for acceleration over time. If we integrate it, we get instantaneous velocity. Now i have taken a limit for time. How will this graph look like?
I have been told that integrating a function provides me with the area under the curve. If i represent this in a linear way (without area), do i get a function which has a periodic increase in rate of change? Now if i want the displacement, I would integrate the function for velocity. As i now have the function for displacement, how will this graph look like?
I understand that it will simply be a graph which increases just like velocity does, but since the graph a = |sin t| after integration, gives us the area under it for velocity, is it possible to represent the displacement in the same graph? Just like velocity was in an a-t graph? If i look at it in terms of dimensions, Its obvious why this happens, its simply because velocity = m/s. And assuming t is in seconds and acceleration in m/s^2, area would naturally give us velocity. But to obtain displacement, i would need to multiply the square of time with the acceleration.
What implications does this have on the graph?
Thank you.
It would be the area under the curve which represents the area under the acceleration curve. There isn't really any particularly easy way to represent this, as far as I know. You could numerically integrate it twice to get a crude approximation, but that's about it.