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Question 258 of 949

Which of the following is a derived quantity in the International System of Units (SI)?

  • Length
  • Time
  • Mass
  • Velocity

Correct Answer: D

Explanation
The correct option is **D. Velocity**. ### Explanation of Why the Answer is Correct In the International System of Units (SI), quantities are classified into two main categories: **base quantities** and **derived quantities**. 1. **Base Quantities**: These are the fundamental physical quantities from which other quantities are derived. The seven base quantities in the SI system are: - Length (meter, m) - Mass (kilogram, kg) - Time (second, s) - Electric current (ampere, A) - Thermodynamic temperature (kelvin, K) - Amount of substance (mole, mol) - Luminous intensity (candela, cd) 2. **Derived Quantities**: These are quantities that are derived from the base quantities through mathematical relationships. Derived quantities often involve combinations of base quantities. **Velocity** is defined as the rate of change of displacement with respect to time. It is calculated using the formula: \[ \text{Velocity} (v) = \frac{\text{Displacement} (s)}{\text{Time} (t)} \] In SI units, displacement is measured in meters (m) and time in seconds (s), so velocity is expressed in meters per second (m/s). Since velocity is derived from the base quantities of length and time, it is classified as a derived quantity. ### Explanation of Why the Other Options are Wrong or Weaker - **A. Length**: Length is a base quantity in the SI system. It is measured in meters (m) and does not depend on any other quantities for its definition. - **B. Time**: Time is also a base quantity in the SI system. It is measured in seconds (s) and is fundamental to the measurement of other quantities. - **C. Mass**: Mass is another base quantity in the SI system. It is measured in kilograms (kg) and serves as a fundamental measure of the amount of matter in an object. ### Summary of Key Points - **Base Quantities**: Length, time, and mass are all base quantities in the SI system. - **Derived Quantity**: Velocity is a derived quantity, calculated from the base quantities of length and time. - **Formula for Velocity**: \( v = \frac{s}{t} \) where \( s \) is displacement and \( t \) is time. - **Units of Velocity**: The SI unit for velocity is meters per second (m/s). ### Revision Summary - **Base quantities** in SI: Length, time, mass, etc. - **Derived quantities** are formed from base quantities (e.g., velocity). - **Velocity** is calculated as displacement over time: \( v = \frac{s}{t} \). - **Correct answer**: D. Velocity is a derived quantity.
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