Answer the following questions. Basic conversion facts: SI = 4 quarters, 10 dimes, 20 nickels, 100 pennies. Quarter =
0.10, nickel =
0.01. 1 hr = 60 min, 1 min = 60 s, 1 hr = 3600 s. (hr: hour; min: minute; s: second) 1 km = 1000 m, 1 m = 100 cm. (km: kilometer; m: meter; cm: centimeter) 1 m = 0.001 km, 1 cm = 0.01 m, 1 m = 100 cm. 1 mile = 1609 m, 1 m = 3.3 ft, 1 ft = 12 in, 1 in = 2.54 cm. (ft: foot; in: inch) 1 mile/hr (1 mph) = 1.609 km/hr. 1 mile/hr = 0.447 m/s. Practice: Car A moves at 6 km/hr, car B moves at 15 mph. Which car moves at the faster speed? In the US, a car’s speedometer records speed in miles per hour as well as km per hour: 70 miles per hour is equal to how many km per hour; or m/s? Miles per hour to km per hour: Miles per hour to m/s:
Answer the following questions. Basic conversion facts: SI = 4 quarters, 10 dimes, 20 nickels, 100 pennies. Quarter =
0.10, nickel =
0.01. 1 hr = 60 min, 1 min = 60 s, 1 hr = 3600 s. (hr: hour; min: minute; s: second) 1 km = 1000 m, 1 m = 100 cm. (km: kilometer; m: meter; cm: centimeter) 1 m = 0.001 km, 1 cm = 0.01 m, 1 m = 100 cm. 1 mile = 1609 m, 1 m = 3.3 ft, 1 ft = 12 in, 1 in = 2.54 cm. (ft: foot; in: inch) 1 mile/hr (1 mph) = 1.609 km/hr. 1 mile/hr = 0.447 m/s. Practice: Car A moves at 6 km/hr, car B moves at 15 mph. Which car moves at the faster speed? In the US, a car’s speedometer records speed in miles per hour as well as km per hour: 70 miles per hour is equal to how many km per hour; or m/s? Miles per hour to km per hour: Miles per hour to m/s:
The Correct Answer and Explanation is:
Answers
- Car B (15 mph) is faster.
15 mph ≈ 24.1 km h⁻¹, while 6 km h⁻¹ ≈ 3.7 mph. - 70 mph conversions
- a. 70 mph ≈ 113 km h⁻¹ (precisely 112.6 km h⁻¹).
- b. 70 mph ≈ 31.3 m s⁻¹.
Why these are the correct numbers
The key to any unit-conversion problem is the conversion factor—a statement that two different numerical values actually represent the same physical quantity. For everyday speed questions involving cars, the two factors that matter most are: 1 mile=1 609 m,1 hour=3 600 s.1\;\text{mile} = 1\,609\;\text{m},\qquad 1\;\text{hour} = 3\,600\;\text{s}.
From these we can pre-compute two handy ratios that appear on most science‐class “cheat sheets”: 1 mph=1.609 km h−1,1 mph=0.447 m s−1.1\;\text{mph} = 1.609\;\text{km h}^{-1},\qquad 1\;\text{mph} = 0.447\;\text{m s}^{-1}.
Question 1
We can compare the two car speeds in either unit system; the trick is to put them in the same units before judging.
Option A (convert Car B to km h⁻¹). 15 mph×1.609 km h−1mph=24.135 km h−1.15\;\text{mph}\times1.609\;\frac{\text{km h}^{-1}}{\text{mph}}=24.135\;\text{km h}^{-1}.
Since 24.1 km h⁻¹ > 6 km h⁻¹, Car B is faster.
Option B (convert Car A to mph). 6 km h−1×11.609 mphkm h−1=3.73 mph,6\;\text{km h}^{-1}\times\frac{1}{1.609}\;\frac{\text{mph}}{\text{km h}^{-1}}=3.73\;\text{mph},
again confirming Car B’s greater speed.
Either path works because multiplication by 1 in the form of a conversion factor doesn’t change the physical meaning—only the numerical representation.
Question 2
For a dashboard that shows both scales, the same factors turn 70 mph into km h⁻¹ and m s⁻¹.
Kilometres per hour. 70 mph×1.609 km h−1mph=112.63 km h−170\;\text{mph}\times1.609\;\frac{\text{km h}^{-1}}{\text{mph}}=112.63\;\text{km h}^{-1}
(rounded to 113 km h⁻¹ for everyday driving).
Metres per second. 70 mph×0.447 m s−1mph=31.29 m s−1.70\;\text{mph}\times0.447\;\frac{\text{m s}^{-1}}{\text{mph}}=31.29\;\text{m s}^{-1}.
Because the conversions involve only multiplication, significant figures track cleanly: two or three significant digits are more than adequate for on-road use.
Take-away techniques
- Write the target unit on paper first, then choose the conversion factor that cancels the original unit.
- Chain factors if you don’t have a one-step shortcut (e.g., mph→m s⁻¹ can be done via mph→km h⁻¹→m s⁻¹).
- Keep an eye on magnitude: a speed in m s⁻¹ will always be a much smaller number than the same speed in km h⁻¹, which in turn is smaller than in mph. That mental check prevents calculator errors.
Mastering this simple factor-label method works just as well for currencies, recipes, and physics labs as it does for comparing whose car is quicker!
