To find the lower and upper bounds of $s$, we begin by determining the upper and lower bounds of $d$ (distance) and $t$ (time).

Step 1: Identify significant figures

Given:

• $d = 190$ metres (2 significant figures)
• $t = 8.1$ seconds (2 significant figures)

Step 2: Find the bounds

For $d$:

• $d = 190$ metres to 2 significant figures means:
  • The lower bound $d_{\text{lower}} = 185$ metres
  • The upper bound $d_{\text{upper}} = 195$ metres

For $t$:

• $t = 8.1$ seconds to 2 significant figures means:
  • The lower bound $t_{\text{lower}} = 8.05$ seconds
  • The upper bound $t_{\text{upper}} = 8.15$ seconds

Step 3: Calculate speed $s = \frac{d}{t}$

Upper bound of $s$:

The upper bound of $s$ occurs when $d$ is at its maximum and $t$ is at its minimum: $s_{\text{upper}} = \frac{d_{\text{upper}}}{t_{\text{lower}}} = \frac{195}{8.05}$

Lower bound of $s$:

The lower bound of $s$ occurs when $d$ is at its minimum and $t$ is at its maximum: $s_{\text{lower}} = \frac{d_{\text{lower}}}{t_{\text{upper}}} = \frac{185}{8.15}$

Let's calculate these values to 3 significant figures.The lower bound of $s$ is approximately $22.7 \, \text{m/s}$, and the upper bound of $s$ is approximately $24.2 \, \text{m/s}$, both rounded to 3 significant figures.

Would you like further details or explanations?

Here are 5 related questions for further practice:

1. How do significant figures impact the accuracy of your final answer?
2. What would happen to the upper and lower bounds of $s$ if $d$ was measured to 3 significant figures instead?
3. Can you calculate the percentage error introduced by rounding $d$ and $t$ to their respective significant figures?
4. How would you find the bounds if $s$ was calculated using a different formula, such as acceleration?
5. What are the implications of having large ranges in upper and lower bounds in real-world applications?

Tip: Always pay close attention to significant figures as they directly affect the precision of your calculated results.