Question

# A body travels uniformly a distance $\left(13.8+0.2\right)m$ in a time $\left(4+0.3\right)s$. Find the velocity of the body within error limits and the percentage error.

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Solution

## Step 1: Given dataThe total distance traveled by the body is $d=13.8$ m.$t=4$ sec.distance error is $∆d=0.2$ m.The total time taken by the body is $\left(4+0.3\right)s$Time error is $∆t=0.3$ sec.Step 2: Error limits and percentage errorSometimes in measurement, there is some uncertainty in determining some quantity, this uncertainty is called an error.The error limits is defined by the form, $\frac{∆v}{v}=\frac{∆d}{d}+\frac{∆t}{t}$, where, $∆v$, $∆d$, and $∆t$ are the errors in velocity, distance, and time respectively.The percentage error is defined by the form, $\frac{∆v}{v}×100$.Step 3: Calculate the velocityThe actual distance traveled as per the question is $\mathrm{d}=13.8\mathrm{m}$And the actual time taken is $\mathrm{t}=4\mathrm{s}$Velocity will be given as: $\mathrm{V}=\frac{\mathrm{distance}}{\mathrm{time}}=\frac{13.8}{4}=3.45{\mathrm{ms}}^{-1}$Step-4: Finding the error limitsError limits in velocity are $\frac{∆v}{v}=\frac{∆d}{d}+\frac{∆t}{t}=\frac{0.2}{13.8}+\frac{0.3}{4}\phantom{\rule{0ex}{0ex}}or\frac{∆v}{v}=0.089$Step 5: Finding the percentage errorThe percentage error in velocity is $\frac{∆v}{v}×100=0.089×100\phantom{\rule{0ex}{0ex}}or\frac{∆v}{v}×100=8.9%$So, the error limit in velocity is $0.089$ and the percentage of error is $8.9%$.

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