To find the uncertainty in distance, given a 0.4% uncertainty in speed (3 m/s), we need to understand how uncertainty propagates through related quantities. Here, we're assuming that distance ($d$) is related to speed ($v$) and time ($t$) by the formula:

$d = v \cdot t$

Now, since you're given the percentage uncertainty in speed, and if we assume there's no uncertainty in time, the percentage uncertainty in distance will be the same as the percentage uncertainty in speed.

Step-by-Step:

1. The uncertainty in speed is 0.4%, or 0.004 in decimal form.
2. The uncertainty in distance will also be 0.4%, as long as time is considered exact.
3. To find the absolute uncertainty in distance, multiply the percentage uncertainty by the distance traveled.

If time is not given, the exact uncertainty in distance can't be calculated, but you know that its percentage uncertainty is 0.4%. So for any distance $d$, the absolute uncertainty in distance ($\Delta d$) is:

$\Delta d = 0.004 \times d$

For example:

• If $d = 10 \, \text{m}$, the uncertainty in distance would be $\Delta d = 0.004 \times 10 = 0.04 \, \text{m}$.

Would you like further details or clarification?

Here are some follow-up questions you might find useful:

1. How do uncertainties combine if both speed and time have uncertainties?
2. What is the formula for uncertainty in a product of two quantities?
3. How would you calculate the percentage uncertainty if both speed and time have uncertainties?
4. Can uncertainty in time also affect the uncertainty in distance?
5. How would uncertainty be affected if velocity were given in vector form?

Tip: When propagating uncertainties, remember that percentage uncertainties in direct multiplicative relationships (like speed and distance) usually remain proportional.