Worked Examples

Worked Examples

Example 1: Basic Speed Calculation

Problem: A car travels 150 km in 2.5 hours. Calculate its average speed.

Solution:

Using S = D ÷ T

Speed = 150 km ÷ 2.5 hours = 60 km/h

Answer: 60 km/h

Example 2: Finding Time with Unit Conversion

Problem: A runner maintains a speed of 8 m/s. How long does it take to run 2.4 km?

Solution:

First convert 2.4 km to metres: 2.4 × 1000 = 2400 m

Using T = D ÷ S

Time = 2400 m ÷ 8 m/s = 300 seconds = 5 minutes

Answer: 5 minutes

Example 3: Density with Unit Conversion

Problem: A gold bar has mass 150 g and volume 7.8 cm³. Calculate its density in both g/cm³ and kg/m³.

Solution:

Using D = M ÷ V

Density = 150 g ÷ 7.8 cm³ = 19.23 g/cm³

Converting to kg/m³: 19.23 × 1000 = 19,230 kg/m³

Answer: 19.23 g/cm³ or 19,230 kg/m³

Example 4: Pressure Calculation

Problem: A force of 500 N is applied over an area of 0.25 m². Calculate the pressure.

Solution:

Using P = F ÷ A

Pressure = 500 N ÷ 0.25 m² = 2000 N/m² = 2000 Pa

Answer: 2000 Pa (or 2 kPa)

Example 5: Multi-Step Journey

Problem: A train travels 80 km in the first hour at 80 km/h, then 120 km in the next 1.5 hours. Calculate the average speed for the whole journey.

Solution:

Total distance = 80 km + 120 km = 200 km

Total time = 1 hour + 1.5 hours = 2.5 hours

Average speed = 200 km ÷ 2.5 hours = 80 km/h

Answer: 80 km/h