d= 180 metres to 2 significant figures
t=7.2 seconds to 2 significant figure
calculate the lower and upper bounds of s
give ur answers to 3 significant figures

The speed \( s \) is calculated using the formula:

\[
s = \frac{d}{t}
\]

Where:
- \( d \) is the distance, and
- \( t \) is the time.

### Step 1: Find the lower and upper bounds for \( d \) and \( t \)
Given that both \( d \) and \( t \) are to 2 significant figures, we need to determine their respective bounds:

- \( d = 180 \) metres to 2 significant figures means \( d \) is in the range:
  \[
  \text{Lower bound of } d = 179.5 \text{ metres}
  \]
  \[
  \text{Upper bound of } d = 180.5 \text{ metres}
  \]

- \( t = 7.2 \) seconds to 2 significant figures means \( t \) is in the range:
  \[
  \text{Lower bound of } t = 7.15 \text{ seconds}
  \]
  \[
  \text{Upper bound of } t = 7.25 \text{ seconds}
  \]

### Step 2: Calculate the lower and upper bounds for \( s \)
Now we calculate the speed \( s \) at both the lower and upper bounds.

#### Lower bound of \( s \):
\[
s_{\text{lower}} = \frac{\text{Lower bound of } d}{\text{Upper bound of } t} = \frac{179.5}{7.25} = 24.759 \, \text{m/s}
\]
(rounded to 3 significant figures: \( 24.8 \, \text{m/s} \))

#### Upper bound of \( s \):
\[
s_{\text{upper}} = \frac{\text{Upper bound of } d}{\text{Lower bound of } t} = \frac{180.5}{7.15} = 25.245 \, \text{m/s}
\]
(rounded to 3 significant figures: \( 25.2 \, \text{m/s} \))

### Final Answer:
- Lower bound of \( s \): \( 24.8 \, \text{m/s} \)
- Upper bound of \( s \): \( 25.2 \, \text{m/s} \)

Do you want more details on how these bounds are determined?

Here are 5 related questions:
1. How do significant figures affect the accuracy of physical measurements?
2. Can you calculate the percentage uncertainty from these bounds?
3. How would rounding to more significant figures change the results?
4. What is the impact of time uncertainty on speed calculations?
5. How do lower and upper bounds apply to real-world engineering problems?

**Tip:** When calculating bounds, always use the maximum possible range to avoid underestimating uncertainty.

d= 180 metres to 2 significant figures, t=7.2 seconds to 2 significant figures. Calculate the lower and upper bounds of s. Give your answers to 3 significant figures.

Learn how to calculate the lower and upper bounds of speed when distance is 180 m and time is 7.2 seconds, both to 2 significant figures. This problem explores key concepts in measurement uncertainty and error propagation, using real-world examples. Suitable for students in Grades 9-12.

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