Compound units: speed, density and pressure

Compound unit problems appear on every OCR J560 paper. They combine two (or more) standard units. The formulae triangle method helps but understanding the underlying relationships is essential for multi-step problems.

Speed, distance and time

Speed = Distance ÷ Time (S = D/T).

Units: metres per second (m/s), kilometres per hour (km/h), miles per hour (mph).

Triangle method: cover the quantity you want — the remaining two show what to do.

• Distance = Speed × Time.
• Time = Distance ÷ Speed.
• Speed = Distance ÷ Time.

Example: A train travels 240 km in 3 hours. Speed = 240 ÷ 3 = 80 km/h.

Example: A cyclist travels at 15 km/h for 2.5 hours. Distance = 15 × 2.5 = 37.5 km.

Average speed

Average speed = Total distance ÷ Total time.

NOT the arithmetic mean of two speeds (common error).

Example: 60 km at 30 km/h, then 60 km at 60 km/h.

• Time for first 60 km = 60/30 = 2 hours.
• Time for second 60 km = 60/60 = 1 hour.
• Average speed = 120/3 = 40 km/h (NOT (30+60)/2 = 45 km/h).

Unit conversions for speed

Converting km/h to m/s: divide by 3.6 (× 1000 ÷ 3600). Converting m/s to km/h: multiply by 3.6.

Example: 90 km/h = 90 ÷ 3.6 = 25 m/s.

Density, mass and volume

Density = Mass ÷ Volume (D = M/V).

Units: grams per cm³ (g/cm³), kilograms per m³ (kg/m³).

• Mass = Density × Volume.
• Volume = Mass ÷ Density.

Example: A block has mass 432 g and volume 60 cm³. Density = 432/60 = 7.2 g/cm³ (iron ≈ 7.87 g/cm³).

Example: Volume of 250 g of aluminium (density 2.7 g/cm³) = 250/2.7 ≈ 92.6 cm³.

Pressure, force and area

Pressure = Force ÷ Area (P = F/A).

Units: Newtons per m² (N/m² = Pascals, Pa), N/cm².

• Force = Pressure × Area.
• Area = Force ÷ Pressure.

Example: A force of 600 N acts on an area of 0.3 m². Pressure = 600/0.3 = 2000 Pa.

Multi-step problems

OCR often combines compound units with other calculations (e.g., find the volume using formulae for G17, then find the mass).

Common OCR exam mistakes

1. Dividing instead of multiplying (or vice versa) — use the triangle to check.
2. Mixing units: time in minutes when formula needs hours; cm when formula needs m.
3. Average speed: averaging the two speeds instead of using total distance ÷ total time.
4. Density: using diameter instead of radius when finding the volume of a cylinder, then dividing mass by wrong volume.