Level 5 · Ages 15–16
Read it again any time, including while you work through the exercises.
You already know speed: kilometres divided by hours. That was only the beginning! Physicists and engineers keep building new quantities by combining existing ones. There are two recipes: dividing or multiplying.
A quotient quantity comes from dividing two quantities. Density divides a mass by a volume: an iron cube of 200 cm³ weighing 540 g would have a density of 540 ÷ 200 = 2.7 g/cm³. Flow rate divides a volume by a duration: a tap filling 120 L in 4 min has a flow rate of 30 L/min.
A product quantity comes from multiplying two quantities. The star is the kilowatt-hour (kWh), the unit on electricity bills: a power (in kW) multiplied by a duration (in h). A 1.5 kW heater running for 3 h uses 1.5 × 3 = 4.5 kWh.
The superpower of these quantities: their units do the thinking for you! In g/cm³, the fraction bar says "grams divided by cubic centimetres". In kWh, the units side by side say "kilowatts multiplied by hours". By reading the unit, you recover the formula.
One last reflex: these formulas flip around. If density = mass ÷ volume, then mass = density × volume. Knowing a compound quantity means juggling its three forms.
An object has a mass of 540 g and a volume of 200 cm³. What is its density?
ρ = m ÷ V
Density is a quotient quantity: the mass divided by the volume.
540 ÷ 200 = 2,7
I divide: 540 ÷ 200 = 2.7. Each cubic centimetre weighs 2.7 grams.
unité : g/cm³
The unit tells the story: grams per cubic centimetre.
Result: The density is 2.7 g/cm³.
A 1500 W heater runs for 3 h. How much energy does it use, in kWh?
1500 W = 1,5 kW
First I convert the power: 1000 W make 1 kW, so 1500 W = 1.5 kW.
E = P × t = 1,5 × 3
Energy is a product quantity: the power multiplied by the duration.
1,5 × 3 = 4,5
I compute: 1.5 × 3 = 4.5. The unit kWh really does say kilowatts × hours.
Result: The heater uses 4.5 kWh.