A body travels uniformly a distance (13.8±0.2)m in a time (4.0±0.3)s. Calculate its velocity with error limits. What is the percentage error in velocity?

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Uploaded: 2022-06-20T20:08:47.000Z
Duration: 9 min
Description: A body travels uniformly a distance (13.8±0.2)m in a time (4.0±0.3)s. Calculate its velocity with error limits. What is the percentage error in velocity?

Given distance s=(13.8±0.2)m and time t=(4.0±0.3)svelocity v=ts=4.013.8=3.45 ms−1=3.5 ms−1vΔv=±[sΔs+tΔt]=±[13.80.2+4.00.3]=±[13.8×4.00.8+4.14]=±13.8×4.04.94=±0.0895Δv=±0.0895×v=±0.0895×3.45=±0.3087=±0.31v=(3.5±0.31)ms−1percentage error in velocity =vΔv×100=±0.0895×100=±8.95%=±9%

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A body travels uniformly a distance (13.8 0.2) {m} in a time

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A body travels uniformly a distance $(13.8 \pm 0.2) m$ in a time $(4.0 \pm 0.3) s$ . Calculate its velocity with error limits. What is the percentage error in velocity?

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Updated on: Jun 20, 2022

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Chloe Discussed

A body travels uniformly a distance

(13.8 \pm 0.2) m

in a time

(4.0 \pm 0.3) s

. Calculate its velocity with error limits. What is the percentage error in velocity?

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Given distance

s = (13.8 \pm 0.2) m

and time

t = (4.0 \pm 0.3) s

velocity

v = \frac{s}{t} = \frac{13.8}{4.0} = 3.45 ms^{- 1} = 3.5 ms^{- 1}

\frac{Δ v}{v} = \pm [\frac{Δ s}{s} + \frac{Δ t}{t}] = \pm [\frac{0.2}{13.8} + \frac{0.3}{4.0}] = \pm [\frac{0.8 + 4.14}{13.8 \times 4.0}] = \pm \frac{4.94}{13.8 \times 4.0} = \pm 0.0895

Δ v = \pm 0.0895 \times v = \pm 0.0895 \times 3.45 = \pm 0.3087 = \pm 0.31 v = (3.5 \pm 0.31) ms^{- 1}

percentage error in velocity

= \frac{Δ v}{v} \times 100 = \pm 0.0895 \times 100 = \pm 8.95%

= \pm 9%

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Question Text	A body travels uniformly a distance $(13.8 \pm 0.2) m$ in a time $(4.0 \pm 0.3) s$ . Calculate its velocity with error limits. What is the percentage error in velocity?
Updated On	Jun 20, 2022
Topic	Units and Measurements
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 1
Upvotes	177
Avg. Video Duration	9 min

A body travels uniformly a distance $(13.8 \pm 0.2) m$ in a time $(4.0 \pm 0.3) s$ . Calculate its velocity with error limits. What is the percentage error in velocity?

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A body travels uniformly a distance (13.8±0.2)m in a time (4.0±0.3)s. Calculate its velocity with error limits. What is the percentage error in velocity?

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A body travels uniformly a distance $(13.8 \pm 0.2) m$ in a time $(4.0 \pm 0.3) s$ . Calculate its velocity with error limits. What is the percentage error in velocity?