10 Common Examples of Direct Variation

The relationship between distance and time, income and hourly wage, weight and mass, speed and distance traveled, pressure and volume, temperature and kinetic energy, and force and acceleration are examples of direct variation in mathematics.

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Examples of Direct Variation

Here are a few Examples of Direct Variation in Math:

1: Flow Rate and Pipe Diameter

Doubling the diameter of a pipe under constant pressure quadruples the fluid flow rate based on the relationship between flow and cross-sectional area.

2: Medication Dose and Body Weight

The dose of medications often scales directly with patient body weight. Heavier patients require corresponding higher doses compared to low body weight patients.

3: Company Revenue and Number of Employees

Hiring more people can directly correlate with increased company productivity and sales revenue since more employees contribute to more output.

4: Distance and Time Traveling at Constant Speed

The distance traveled is directly proportional to the time spent traveling if speed is constant. For example, traveling twice as long means covering twice the distance.

5: Light Intensity and Distance from Source

The intensity of light from a point source decreases proportionally as distance from the source increases according to the inverse square law.

6: Volume and Radius of Sphere

For a sphere of fixed proportions, volume increases or decreases directly as radius cubed. Having twice the radius means 2^3 = 8 times the volume.

7: Force and Area under Pressure

For a constant pressure, the perpendicular force applied is directly proportional to the area over which the pressure is applied.

8: Friction Force and Normal Force

The friction force between two solid surfaces is directly proportional to the normal force pressing them together as per Coulomb’s law of friction.

9: Braking Distance and Speed

The braking distance required for a vehicle is directly proportional to its speed, assuming a constant braking force. Doubling the vehicle’s velocity will double the distance needed to come to a stop.

10: Temperature Change and Mass

For an object with constant specific heat capacity, the temperature change the object undergoes will vary directly with the amount of heat transferred. Since heat equals mass times specific heat capacity times temperature change, temperature change depends directly on mass at a constant specific heat.

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