Question about calculus my dad made me think about

[HorseRidingTic]

This is a question I'v got about calculus after doing my bachelors in engineering degree.

So you can integrate an acceleration graph to get velocity, and integrate a velocity graph to get distance.
Integrating a graph can be done by easily finding the area under the graph.
This applies to all polynomial graphs.

So what about analog type recorded information graphs.
Say if you were kidnapped and driven around Rio de Jarinro (a made up city that is just one giant long road going into the Amazon) in the boot of a car with only an accelerometer in your pocket recording an acceleration time graph. If you used a program on your computer to work out the area under the graph, would this plot velocity, and then distance?
If so, what maths programs can measure the area under an analog graph?

Thanks,
neb

 

[jedishrfu]

You would have to do this numerically as you don’t have a well known curve.

There’s a simple physics experiment that utilizes this approach called the Atwood machine experiment where you drop a weight with an oscillating pen. As the weight falls the pen traces out a stretched sine curve. You measure the distances between the peak and use the time of one complete oscillation and from that can determine the acceleration, velocity and distance traveled.

In your case, you need to record the time and the accelerometer value and then do the math. If you plot it on graph paper you can add up the squares to get the areas or you can make trapezoids from each successive measurement and plot the areas to get th velocity athen repeat to get the distances at each time.

 

[berkeman]

what maths programs can measure the area under an analog graph?

The simplest is probably just to use Excel. Are you familiar with how to do simple integrations like this with an Excel spreadsheet?

 

[FactChecker]

That works in practice for a short time and in theory for a long time. But it does not work well in practice over a long length of time. Over a short time, a small error in acceleration can integrate to a small error in velocity and then to a small error in position. But over a long time, the velocity remains wrong and the error in position keeps growing till it is way off. That is why airplanes before GPS which relied on accelerometers had to periodically take "fixes" on known ground positions to correct the growing position errors. (There are other sources of errors from accelerometer-based inertial reference systems, but that gets advanced very quickly.)