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define-derived-physical-quantities

🚀 Derived physical quantities are quantities that are derived from the fundamental physical quantities through mathematical relationships. In physics, we have seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Derived quantities are formed by combining these base quantities using multiplication, division, or exponentiation. Examples of derived quantities include area, volume, speed, acceleration, force, and energy.

Theory Explanation

Understanding Base and Derived Quantities

Base quantities are the fundamental quantities that cannot be expressed in terms of other quantities. Derived quantities, on the other hand, are formed from these base quantities. For example, speed is derived from distance (length) and time.

Formulating Derived Quantities

To derive a physical quantity, we use mathematical operations on base quantities. For instance, the area (A) is derived from length (L) as A = L × L, and the unit of area is square meters (m²). Similarly, speed (v) is derived from distance (d) and time (t) as v = d/t, with units of meters per second (m/s).

\[ v = \frac{d}{t} \]

Key Points

  • 🎯 Derived quantities are formed from base quantities.
  • 🎯 Common derived quantities include area, volume, speed, and force.
  • 🎯 Units of derived quantities are combinations of the units of base quantities.

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Examples:💡

Calculate the speed of an object that travels 100 meters in 5 seconds.

Solution:

Step 1: Identify the distance and time: Distance (d) = 100 m, Time (t) = 5 s.

Step 2: Use the formula for speed: v = d/t.

Step 3: Substitute the values: v = 100 m / 5 s = 20 m/s.

Step 4: Thus, the speed of the object is 20 m/s.

Common Mistakes

  • Mistake: Confusing base quantities with derived quantities.

    Correction: Remember that base quantities are fundamental and cannot be derived from others, while derived quantities are formed from base quantities.

  • Mistake: Incorrectly applying the formulas for derived quantities.

    Correction: Always double-check the formula and ensure that you are using the correct base quantities.

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