# Uncertainty calculations. [closed]

Can anyone please clarify what I need to do here:

$$s=ut+\frac{1}{2}at^{2}$$

Assume that the initial velocity, acceleration and the time have been measured, along with their respective uncertainties (see the table below). Using the rules for propagation of uncertainties through calculations, calculate the displacement of the body at the given time along with its uncertainty. State the uncertainty both in absolute terms and also as a percentage (relative) uncertainty

Calculate the absolute and percentage uncertainty in the calculated displacement, s, at a time, t, showing your calculation in full. Show the correct number of significant figures in your results. (It is permissible to carry a greater number of figures than are significant during your calculation to avoid loss of precision.)

## closed as off-topic by Kyle Kanos, Jon Custer, peterh, Yashas, FlorisMar 13 '17 at 16:04

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Kyle Kanos, Jon Custer, peterh, Yashas, Floris
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• Do you know how the rules of propagate of error work? You have errors in the three variables. The product $ut$ has a combined error (how do you combine errors when multiplying?); the product $\frac12 a t^2$ has another error (multiplying three things with error in them). Finally, you add them (combine errors for sum). – Floris Mar 13 '17 at 16:03

For addition/subtraction: $$A = B + C$$ $$\sigma_{A} = \sqrt{\sigma_{B}^{2} + \sigma_{C}^{2} }$$ For multiplication/division $$A = \frac{B \times C}{D}$$ $$\sigma_{A} = A \sqrt{(\frac{\sigma_{B}}{B})^{2} + (\frac{\sigma_{C}}{C})^{2} + (\frac{\sigma_{D}}{D})^{2} }$$
Your equation is (it seems) $$s=ut+\frac{1}{2}at^2$$ So you need to break this down into its different components, multiplication and addition, and calculate the errors on those to eventually get an error $\sigma_{s}$ in the end. If you struggle with this, let me know where but make sure you try it yourself first.
Note that constants (ie the $\frac{1}{2}$) will have no error.