Determine how long it will take to travel 500.0 miles if you are traveling at 3.0 m/s. 1 inch=2.54cm and 1 mile=5280 ft. In seconds (Why is it 2 significant figures?)

To determine how long it will take to travel 500.0 miles at a speed of 3.0 m/s, we first need to convert the distance from miles to meters, and then use the formula for time:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]

### Step 1: Convert miles to meters

1 mile = 5280 feet  
1 foot = 12 inches  
1 inch = 2.54 cm  
1 meter = 100 cm

First, convert miles to feet:

\[
500.0 \text{ miles} \times 5280 \text{ feet/mile} = 2,640,000 \text{ feet}
\]

Next, convert feet to inches:

\[
2,640,000 \text{ feet} \times 12 \text{ inches/foot} = 31,680,000 \text{ inches}
\]

Convert inches to centimeters:

\[
31,680,000 \text{ inches} \times 2.54 \text{ cm/inch} = 80,467,200 \text{ cm}
\]

Finally, convert centimeters to meters:

\[
80,467,200 \text{ cm} \times \frac{1 \text{ meter}}{100 \text{ cm}} = 804,672 \text{ meters}
\]

### Step 2: Calculate the time

Now that we have the distance in meters, we can calculate the time using the formula:

\[
\text{Time} = \frac{804,672 \text{ meters}}{3.0 \text{ m/s}} = 268,224 \text{ seconds}
\]

### Why 2 Significant Figures?

The original speed was given as 3.0 m/s, which has two significant figures. The distance of 500.0 miles has four significant figures. However, when multiplying or dividing quantities, the result should be reported with the same number of significant figures as the quantity with the fewest significant figures, which in this case is the speed (3.0 m/s). Therefore, the time should be reported with 2 significant figures.

### Final Answer
\[
\text{Time} \approx 270,000 \text{ seconds}
\]

Do you want details or have any questions?

Here are 5 relative questions to expand your understanding:

1. How do significant figures affect calculations in physics and engineering?
2. What are some other common unit conversions used in physics?
3. How would the time change if the speed was doubled?
4. What would the time be if the distance was measured in kilometers instead?
5. How does the precision of measurements impact the accuracy of calculations?

**Tip:** Always keep track of significant figures in your calculations to ensure your results are as accurate as your initial data allows.

Learn how to calculate the time required to travel 500.0 miles at a speed of 3.0 m/s with detailed step-by-step calculations. Understand unit conversions, significant figures, and their impact on accurate results. Suitable for Grades 10-12 students and those interested in physics and engineering calculations.

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