What do you mean by this? Do you mean that there is an intial error of 0.0001 and then after 30 minutes the error becomes 0.0001- 0.00005= 0.00009? And what do you mean by "in one direction"? In what direction? Or is it to be assumed that all motion is in one direction?gkraju said:Homework Statement
In an inertial navigation system on switching ON an intial error of 0.0001m/s^-2 exists in one direction.
After 30 minutes an additional error of -0.00005m/s^-2 in acceleration builds up.
Assuming what I have said above, after the first 30 minutes, the acceleration is a+ .0001 so the velocity will be 30(60)(a+ .0001)= 1800a+ 1.8 so there is an error of 1.8 m/s in the velocity. The distance traveled is 30(180)(1800a+ 1.8)= 3240000a+ 32400 so there is an error of 32400 m in distance traveled.The system navigates for 2hrs 30 minutes after switching ON. compute the error in velocity and distance after every 30 minutes for this navigation
There are three main types of errors in scientific measurements: systematic, random, and gross errors. Systematic errors are caused by flaws in the experimental setup or measurement techniques and can lead to consistent inaccuracies. Random errors, also known as statistical errors, are caused by natural variations in the measurement process and can be reduced by taking multiple measurements. Gross errors are caused by human mistakes or equipment malfunctions and can significantly affect the accuracy of the measurement.
The percent error is calculated by subtracting the accepted or true value from the measured value, dividing the result by the accepted value, and then multiplying by 100. The formula is: percent error = (measured value - accepted value) / accepted value x 100. This value indicates the percentage of error in the measurement, with a lower percent error indicating a more accurate measurement.
Approximations are used in scientific calculations to simplify complex equations and make them more manageable. In some cases, exact solutions may be impossible to obtain, and approximations can provide a reasonable estimate. Additionally, approximations can save time and resources in calculations and allow for faster analysis of data.
Absolute error is the difference between the measured value and the true value, whereas relative error is the ratio of the absolute error to the true value. Absolute error is expressed in the same units as the measurement, while relative error is expressed as a percentage. Relative error is useful for comparing the accuracy of different measurements, while absolute error provides a more precise measure of the magnitude of the error.
To minimize errors in scientific experiments, it is essential to carefully design and control the experimental setup, use precise and calibrated equipment, and take multiple measurements. Additionally, it is crucial to identify and account for any sources of error and to use appropriate mathematical techniques to analyze the data. Collaborating with other scientists and peer-reviewing experimental methods can also help identify potential errors and improve the accuracy of scientific results.