With dimensional analysis, you track units through each conversion until only the requested units remain. For acceleration, “per second squared” puts time squared in the denominator, so the seconds-to-hours factor must be squared. Convert meters to kilometers separately, then type the checked number chain into Desmos. Using the hour factor only once is the tempting trap.
Hints
- Hint 1
A conversion factor is a fraction equal to because its top and bottom name the same amount. Meters start on top of the acceleration. Where should meters go in the factor that changes them to kilometers?
- Hint 2
The denominator is seconds squared, not seconds. That means you must replace two copies of seconds. Put seconds on top of the time factor to cancel them, then raise that whole factor to what power?
- Hint 3
Check the units before calculating: only kilometers on top and hours squared on the bottom should remain. Desmos calculates numbers, not units, so type the numbers from the conversion chain you checked.
Step-by-step
Cancel the units, then calculate
Step 1Read the squared time unit
“Per second squared” means divide by seconds squared, so write the given acceleration as . The applies to seconds in the denominator, not to the meters or the .
- Step 2
Change meters to kilometers
A conversion factor equals because its top and bottom name the same distance. Put meters on the bottom so they cancel the meters on top: .
- Step 3
Change seconds squared to hours squared
Seconds are on the bottom, so put seconds on top of the next factor. There are two copies of seconds to cancel, so square the whole time factor, numbers and units together: . Using only once would convert one second.
- Step 4
Calculate the converted acceleration
Type into Desmos. It shows . The units you checked make the drone’s acceleration kilometers per hour squared. Choice C.