Understanding SI Derived Units for Velocity

This solution explains how to identify the correct SI derived unit for velocity, using only SI base units. Velocity measures how fast an object is moving and in what direction. The International System of Units (SI) provides a standard way to measure physical quantities.

Definition of Velocity and SI Units

Velocity is defined as the rate of change of an object's position (displacement) with respect to time. Mathematically, it can be expressed as:

$ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} $

To find the SI unit for velocity, we need to use the SI base units for the quantities involved:

• The SI base unit for displacement (a measure of length) is the meter ($m$).
• The SI base unit for time is the second ($s$).

Combining these base units according to the definition of velocity gives us the SI derived unit.

Analyzing the Given Options for Velocity Unit

Let's examine each option provided to see which one correctly represents the SI derived unit for velocity using only SI base units:

• Option 1: $m \cdot s$

  This unit represents the product of meters and seconds. It does not correspond to the definition of velocity (displacement divided by time).

• Option 2: $m/s$

  This unit represents meters per second. It is derived by dividing the SI base unit for length ($m$) by the SI base unit for time ($s$). This directly matches the definition of velocity ($ \frac{\text{Displacement}}{\text{Time}} $). Therefore, $m/s$ is the correct SI derived unit for velocity.

• Option 3: $m/s^2$

  This unit represents meters per second squared. It is derived by dividing the unit for velocity ($m/s$) by time ($s$), resulting in $ \frac{m/s}{s} = \frac{m}{s^2} $. This is the SI derived unit for acceleration, not velocity.

• Option 4: $km/h$

  This unit represents kilometers per hour. While $km/h$ is a common unit used to express velocity in everyday contexts (like speed limits), it is not strictly composed of only the fundamental SI base units. The SI base unit for length is the meter ($m$), not the kilometer ($km$), and the SI base unit for time is the second ($s$), not the hour ($h$). Although it can be converted to $m/s$, it's not the representation using *only* SI base units.

Derivation of the SI Unit for Velocity

As established, velocity is displacement over time. Using the SI base units:

$ \text{Unit of Velocity} = \frac{\text{Unit of Displacement}}{\text{Unit of Time}} = \frac{m}{s} $

This shows that the expression $m/s$ is correctly formed using the SI base unit for length ($m$) and the SI base unit for time ($s$).

Conclusion

Based on the definition of velocity and the requirement to use only SI base units (meter $m$ and second $s$), the correct SI derived unit for velocity is meters per second ($m/s$).