Question

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

Answer 1

Step 1: Given data

1. The total distance traveled by the body is $d=13.8$ m.$t=4$ sec.
2. distance error is $∆d=0.2$ m.
3. The total time taken by the body is $(4+0.3)s$
4. Time error is $∆t=0.3$ sec.

Step 2: Error limits and percentage error

1. Sometimes in measurement, there is some uncertainty in determining some quantity, this uncertainty is called an error.
2. 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.
3. The percentage error is defined by the form, $\frac{∆v}{v}\times 100$.

Step 3: Calculate the velocity

1. The actual distance traveled as per the question is $\mathrm{d}=13.8\mathrm{m}$
2. And the actual time taken is $\mathrm{t}=4\mathrm{s}$
3. 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 limits

Error limits in velocity are

$$\begin{gathered} \frac{∆v}{v}=\frac{∆d}{d}+\frac{∆t}{t}=\frac{0.2}{13.8}+\frac{0.3}{4} \\ or\frac{∆v}{v}=0.089 \end{gathered}$$

Step 5: Finding the percentage error

The percentage error in velocity is

$$\begin{gathered} \frac{∆v}{v}\times 100=0.089\times 100 \\ or\frac{∆v}{v}\times 100=8.9\% \end{gathered}$$

So, the error limit in velocity is $0.089$ and the percentage of error is $8.9\%$.