First slide

Accuracy; precision of instruments and errors in measurements

Question

A body travels uniformly a distance of $(13.8 \pm 0.2) m$ in a time $(4.0 \pm 0.3) s$ . The velocity of the body within error limit is

Moderate

A

$(3.45 \pm 0.2) {ms}^{- 1}$
B

$(3.45 \pm 0.3) {ms}^{- 1}$
C

$(3.45 \pm 0.4) {ms}^{- 1}$
D

$(3.45 \pm 0.5) {ms}^{- 1}$

Solution

$v = \frac{d}{t} = \frac{13.8}{4.0} = 3.45 {ms}^{- 1}$
$\frac{Δ v}{v} = \frac{Δ d}{d} + \frac{Δ t}{t}$
$Δ v = [\frac{Δ d}{d} + \frac{Δ t}{t}] v$
$= [\frac{0.2}{13.8} + \frac{0.3}{4}] (3.45) = 0.3 m / s$
$(v \pm Δ v) = (3.45 \pm 0.3) {ms}^{- 1}$

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