Questions: The top speed of a Pontiac GTO 6.0 is 170.26 mph. Given that 1 km = 0.62137 mi and 1 hr = 60 min = 60 s, how fast is this in km / s? Express your answer using the correct number of significant digits. 1.0117 × 10^-6 km / s 1.01 × 10^-6 km / s 0.076113 km / s 0.0761131 km / s

The top speed of a Pontiac GTO 6.0 is 170.26 mph. Given that 1 km = 0.62137 mi and 1 hr = 60 min = 60 s, how fast is this in km / s? Express your answer using the correct number of significant digits. 1.0117 × 10^-6 km / s 1.01 × 10^-6 km / s 0.076113 km / s 0.0761131 km / s
Transcript text: The top speed of a Pontiac GTO 6.0 is $\mathbf{1 7 0 . 2 6 ~ m p h . ~ G i v e n ~ t h a t ~} 1 \mathbf{k m}=$ 0.62137 mi and $1 \mathrm{hr}=60 \mathrm{~min}=60 \mathrm{~s}$, how fast is this in $\mathrm{km} / \mathrm{s}$ ? Express your answer using the correct number of significant digits. $1.0117 \times 10^{-6} \mathrm{~km} / \mathrm{s}$ $1.01 \times 10^{-6} \mathrm{~km} / \mathrm{s}$ $0.076113 \mathrm{~km} / \mathrm{s}$ $0.0761131 \mathrm{~km} / \mathrm{s}$
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Solution

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Solution Steps

Step 1: Convert Miles per Hour to Kilometers per Hour

To convert the speed from miles per hour (mph) to kilometers per hour (km/h), use the conversion factor \(1 \, \text{km} = 0.62137 \, \text{mi}\).

\[ \text{Speed in km/h} = 170.26 \, \text{mph} \times \frac{1 \, \text{km}}{0.62137 \, \text{mi}} \]

Step 2: Calculate the Conversion

Perform the calculation from Step 1 to find the speed in kilometers per hour.

\[ \text{Speed in km/h} = 170.26 \times \frac{1}{0.62137} \approx 274.000 \, \text{km/h} \]

Step 3: Convert Kilometers per Hour to Kilometers per Second

To convert the speed from kilometers per hour (km/h) to kilometers per second (km/s), use the conversion factor \(1 \, \text{hr} = 3600 \, \text{s}\).

\[ \text{Speed in km/s} = \frac{274.000 \, \text{km/h}}{3600 \, \text{s/hr}} \]

Step 4: Calculate the Final Conversion

Perform the calculation from Step 3 to find the speed in kilometers per second.

\[ \text{Speed in km/s} = \frac{274.000}{3600} \approx 0.0761111 \, \text{km/s} \]

Step 5: Determine the Correct Significant Digits

Round the result to the appropriate number of significant digits based on the given options.

The correct answer is \(0.076113 \, \text{km/s}\).

Final Answer

\(\boxed{0.076113 \, \text{km/s}}\)

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