Calculate the uncertainty in the velocity of a wagon of mass 4000kg whose position is known accurately of ± 10 m.

Explanation

To calculate the uncertainty in the velocity of a wagon with a known mass and position uncertainty, we can use the Heisenberg Uncertainty Principle. The formula we will use is:

\[ \Delta V \geq \frac{h}{4\pi m \Delta x} \]

Where:
- \(\Delta V\) is the uncertainty in velocity,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(m\) is the mass of the wagon,
- \(\Delta x\) is the uncertainty in position.

### Step-by-step Solution:

1. **Identify the values:**
- Mass of the wagon, \(m = 4000 \, \text{kg}\)
- Uncertainty in position, \(\Delta x = 10 \, \text{m}\)
- Planck's constant, \(h = 6.626 \times 10^{-34} \, \text{Js}\)

2. **Substitute the values into the formula:**
\[ \Delta V \geq \frac{6.626 \times 10^{-34}}{4\pi \times 4000 \times 10} \]

3. **Calculate the denominator:**
- Calculate \(4\pi\):
\[ 4\pi \approx 12.566 \]
- Calculate \(4\pi \times 4000 \times 10\):
\[ 12.566 \times 4000 \times 10 = 502640 \]

4. **Calculate the uncertainty in velocity:**
\[ \Delta V \geq \frac{6.626 \times 10^{-34}}{502640} \]
- Perform the division:
\[ \Delta V \geq 1.316 \times 10^{-39} \, \text{m/s} \]

5. **Final result:**
The uncertainty in the velocity of the wagon is approximately:
\[ \Delta V \approx 1.316 \times 10^{-39} \, \text{m/s} \]

### Summary:
The uncertainty in the velocity of the wagon is \(1.316 \times 10^{-39} \, \text{m/s}\).