A body travels uniformly a distance of `(20.0 pm 0.2)m` in time `(4.0 pm 0.04)s`. The velocity of the body is

Options

A. `(5.0 pm 0.4) ms^(-1)`
B. `(5.0 pm 0.2) ms^(-1)`
C. `(5.0 pm 0.6) ms^(-1)`
D. `(5.0 pm 0.1) ms^(-1)`

Answer

To solve the problem of finding the velocity of a body that travels a distance of \( (20.0 \pm 0.2) \, m \) in a time of \( (4.0 \pm 0.04) \, s \), we will follow these steps:

### Step 1: Calculate the Velocity
The formula for velocity \( v \) is given by:
\[ v = \frac{\text{distance}}{\text{time}} \]
Substituting the values:
\[ v = \frac{20.0 \, m}{4.0 \, s} = 5.0 \, m/s \]

### Step 2: Calculate the Percentage Error in Distance
The percentage error in distance can be calculated using the formula:
\[ \text{Percentage Error in Distance} = \left( \frac{\Delta d}{d} \right) \times 100 \]
Where \( \Delta d = 0.2 \, m \) and \( d = 20.0 \, m \):
\[ \text{Percentage Error in Distance} = \left( \frac{0.2}{20.0} \right) \times 100 = 1\% \]

### Step 3: Calculate the Percentage Error in Time
Similarly, the percentage error in time is calculated as:
\[ \text{Percentage Error in Time} = \left( \frac{\Delta t}{t} \right) \times 100 \]
Where \( \Delta t = 0.04 \, s \) and \( t = 4.0 \, s \):
\[ \text{Percentage Error in Time} = \left( \frac{0.04}{4.0} \right) \times 100 = 1\% \]

### 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:
\[ \text{Percentage Error in Velocity} = \text{Percentage Error in Distance} + \text{Percentage Error in Time} \]
\[ \text{Percentage Error in Velocity} = 1\% + 1\% = 2\% \]

### Step 5: Calculate the Absolute Error in Velocity
To find the absolute error in velocity, we calculate:
\[ \Delta v = \left( \frac{\text{Percentage Error in Velocity}}{100} \right) \times v \]
Substituting \( v = 5.0 \, m/s \):
\[ \Delta v = \left( \frac{2}{100} \right) \times 5.0 = 0.1 \, m/s \]

### Step 6: Final Result
Now we can express the velocity with its uncertainty:
\[ v = 5.0 \pm 0.1 \, m/s \]

### Conclusion
The final answer is:
\[ \text{Velocity of the body} = 5.0 \pm 0.1 \, m/s \]