physics speed and velocity

Question

The posted speed limit on the road heading from your house to school is 45 mi/h, which is about 20 m/s. If you live 8 km (8,000 m) from school, how long will it take you to get to school if there is no traffic? Convert your answer to minutes.

Answer 1

Any values that contain more than 1 unit are consider conversion factors, because they help you convert from 1 unit to another. As such, conversion factors should never be the first term in your algebraic equation. So we will NOT start with 45 mi/h or 20 m/s. Our choices are 8km or 8000m. I will start with 8000m because there's 1 conversion factor that shares the same unit (m)

#1 (8000m) * (1s/20m) = 400s

When set up the equation, you dont want the same unit in the numerator or denominator. If we start with 8000m, unit (m) has to be in the numerator. If we were to set up the equation as below

#2 (8000m) * (20m/s)

unit (m) appears in the numerator twice, and the result (160,000 m^2/s) is a physics disaster, because (I assume) you havent seen this unit in class :). So we will flip the conversion factor from 20m/s to 1s/20m.

If we set the equation like #1, we have 400s which is a lot more useful because it answers the question in the prompt. Now you just have to convert it into minutes. To go from 1 unit to another, we again use conversion factors. There are 60 sec in 1 min so our conversion factor is 60s/minute. If we start with 400s, we cannot use 60s/minute because we'll have unit (s) in the numerator twice again. So we have to use 1 min / 60 sec

(400s) * (1 minute/60s) = 7 minutes (remember to report the correct number of significant figures in your answer)