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Physics - Basic Uncertanties Question?

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    AB is measured using a metre stick.
    A trolley is timed between AB.

    The following results were obtained - AB = (60+- 0.1)cm

    Times (Seconds) - 1.21, 1.21, 1.26, 1.27, 1.24 and 1.28

    Express the average speed in the form: Value +- Absolute Uncertainty
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    (Original post by nerd434)
    AB is measured using a metre stick.
    A trolley is timed between AB.

    The following results were obtained - AB = (60+- 0.1)cm

    Times (Seconds) - 1.21, 1.21, 1.26, 1.27, 1.24 and 1.28

    Express the average speed in the form: Value +- Absolute Uncertainty
    Well, what are you stuck on?


    First, get an average value for the time taken, and the associated uncertainty (random uncertainty).

    Random UncertaintyFor secondary school uncertainties, I think I recall taking:

    \text{random uncertainty\ }=\frac{\text{max.\ reading\ }- \text{\ min.\ reading}}{\text{number\ of\ readings}}

    However, you might be using the standard error, which is the standard deviation of the given readings divided by the square root of the number of readings.

    Once you have the value for the average time taken (and uncertainty), you can calculate the average speed as the measured distance over the average time taken. The corresponding uncertainty will be given by the formula:

    \frac{\Delta S}{S} = \sqrt{\left( \frac{\Delta D}{D} \right)^2 + \left( \frac{\Delta T}{T} \right)^2},

    where S is the average speed, D is the measured distance, T is the average time, and ΔS, ΔD, ΔT are the absolute uncertainties in those quantities, respectively. :yep:

    Remember that the units for the speed will be carried over from the distance and time measurements (speed will be in cm/s).

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