Understanding rates is crucial in our daily lives, as they help us solve problems related to pressure, density, population density, and movement. This section will guide you through these concepts with practical examples to enhance your problem-solving skills.

Pressure

Pressure is defined as the force exerted per unit area. The formula to calculate pressure is:

• Units: Newton per square meter (N/m²) or Pascals (Pa)

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Example 1: Calculating Pressure

A book weighing 1.5 kg rests on a table with a surface area of 0.5 m². Calculate the pressure exerted by the book on the table.

Solution:

Force exerted by the book = Mass × Gravity

Density

Density is the mass per unit volume of a substance. The formula to calculate density is:

• Units: kilograms per cubic meter (kg/m³)

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Example 2: Calculating Density

Find the density of an object with a mass of 200g and a volume of 50cm³.

Solution:

• Convert mass to kg: $200 \, \text{g} = 0.2 \, \text{kg}$
• Convert volume to $m^3$: $50 \, \text{cm}^3 = 0.00005 \, \text{m}^3$
• $\text{Density} = \frac{0.2 \, \text{kg}}{0.00005 \, \text{m}^3} = 4000 \, \text{kg/m}^3$

Population Density

Population density measures the number of individuals living per unit area. The formula is:

• Units: individuals per square kilometer (people/km²)

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Example 3: Calculating Population Density

Calculate the population density of a city with a population of 500,000 and an area of 250 km².

Solution:

Speed/Distance/Time

The relationship between speed, distance, and time is fundamental in understanding rates of movement. The formula is:

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Example 4: Using the Speed/Distance/Time Formula

If a car travels 300 km in 4 hours, what is its average speed?

Solution: