Three straight segments of a jogging track are measured with the following results:…

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

Three straight segments of a jogging track are measured with the following results: Segment 1: 12.45 cm (±0.03 cm)12.45\,\text{cm}\,(\pm0.03\,\text{cm}) Segment 2: 15.3 cm (±0.1 cm)15.3\,\text{cm}\,(\pm0.1\,\text{cm}) Segment 3: 8.276 cm (±0.005 cm)8.276\,\text{cm}\,(\pm0.005\,\text{cm}) (i) Calculate the total length of the track formed by these three segments. (ii) Determine the absolute uncertainty in the total length. (iii) Express the final length with its uncertainty, rounded to the proper number of decimal places and written in the form value±uncertainty\text{value} \pm \text{uncertainty}. State both the length and its uncertainty in centimetres.

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