To determine which expression correctly describes force using SI units, let’s first understand the standard unit of force. In the International System of Units (SI), force is measured in Newtons (N).
The Newton (N) is defined as the force required to accelerate a one-kilogram mass by one meter per second squared. Therefore, the definition of a Newton can be expressed using the base SI units as follows:
[tex]\[ 1 \, \text{N} = 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}^2} \][/tex]
Now, let's go through the options provided:
A. [tex]\( 1 \, \text{J} = 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \)[/tex]
- This expression defines the Joule (J), which is a unit of energy, not force.
B. [tex]\( 1 \, \text{N} = 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}^2} \)[/tex]
- This expression correctly describes the Newton, aligning with our definition.
C. [tex]\( 1 \, \text{N} = 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}} \)[/tex]
- This expression is incorrect because it describes momentum, not force. Momentum has the units of mass times velocity.
D. [tex]\( 1 \, \text{J} = 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}^2} \)[/tex]
- This expression is incorrect because it mixes units of force (which this form resembles) with energy units; Joule should be related to work or energy, which is [tex]\( 1 \, \text{J} = 1 \, \text{kg} \cdot \frac{\text{m}^2}{\text{s}^2} \)[/tex].
Given the reasoning above, the correct expression that describes force using SI units is:
[tex]\[ \boxed{B} \][/tex]
Thus, the answer is option B:
[tex]\[ 1 \, \text{N} = 1 \, \text{kg} \cdot \frac{\text{m}}{\text{s}^2} \][/tex]
