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.