A body travels uniformly a distance of `13.8 ± 0.2 m` in time `4.0 ± 0.3 s`. The velocity of the body within error limits is?
The percentage errors in the above problem is?

Options

A. `7%`
B. `5.95%`
C. `8.95%`
D. `9.85%`

Explanation

To find the velocity of the body and its percentage error, we will follow these steps:

### Step 1: Calculate the velocity
The formula for velocity \( v \) is given by:
\[ v = \frac{d}{t} \]
where \( d \) is the distance traveled and \( t \) is the time taken.

Given:
- Distance \( d = 13.8 \, \text{m} \)
- Time \( t = 4.0 \, \text{s} \)

Substituting the values:
\[ v = \frac{13.8 \, \text{m}}{4.0 \, \text{s}} = 3.45 \, \text{m/s} \]

### Step 2: Calculate the percentage error in distance
The percentage error in distance can be calculated using the formula:
\[ \text{Percentage Error in Distance} = \left( \frac{\text{Error in Distance}}{\text{Distance}} \right) \times 100 \]
Given the error in distance is \( 0.2 \, \text{m} \):
\[ \text{Percentage Error in Distance} = \left( \frac{0.2}{13.8} \right) \times 100 \approx 1.45\% \]

### Step 3: Calculate the percentage error in time
The percentage error in time can be calculated using the formula:
\[ \text{Percentage Error in Time} = \left( \frac{\text{Error in Time}}{\text{Time}} \right) \times 100 \]
Given the error in time is \( 0.3 \, \text{s} \):
\[ \text{Percentage Error in Time} = \left( \frac{0.3}{4.0} \right) \times 100 = 7.5\% \]

### Step 4: Calculate the total percentage error in velocity
The total percentage error in velocity is the sum of the percentage errors in distance and time:
\[ \text{Total Percentage Error in Velocity} = \text{Percentage Error in Distance} + \text{Percentage Error in Time} \]
Substituting the values:
\[ \text{Total Percentage Error in Velocity} = 1.45\% + 7.5\% = 8.95\% \]

### Final Result
Thus, the velocity of the body is \( 3.45 \, \text{m/s} \) and the percentage error in velocity is approximately \( 8.95\% \).

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