To determine which expression correctly describes energy using SI units, we need to understand the definition of a Joule (J). The Joule is the SI unit of energy defined by the work done when a force of one Newton displaces an object by one meter in the direction of the force. This can be expressed as:
[tex]\[ \text{Energy (J)} = \text{Force (N)} \times \text{Displacement (m)} \][/tex]
Next, we need to recall the definition of a Newton (N), the SI unit of force. One Newton is defined as the force required to accelerate a mass of one kilogram (kg) by one meter per second squared (m/s²):
[tex]\[ \text{Force (N)} = \text{Mass (kg)} \times \text{Acceleration (m/s²)} \][/tex]
Combining these two definitions, we can substitute the expression for force into the expression for energy:
[tex]\[ \text{Energy (J)} = (\text{Mass (kg)} \times \text{Acceleration (m/s\(^2\)})) \times \text{Displacement (m)} \][/tex]
[tex]\[ \text{Energy (J)} = \text{Mass (kg)} \times \text{Acceleration (m/s\(^2\))} \times \text{Displacement (m)} \][/tex]
Since acceleration (m/s²) multiplied by displacement (m) gives us velocity squared (m²/s²):
[tex]\[ \text{Energy (J)} = 1 \, \text{kg} \times 1 \, \text{m}^2 / \text{s}^2 \][/tex]
Hence:
[tex]\[ 1 \, \text{J} = 1 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 \][/tex]
Therefore, the correct expression is:
[tex]\[ \boxed{1 \, \text{J} = 1 \, \text{kg} \cdot \text{m}^2 / \text{s}^2 } \][/tex]
So, the correct option is:
A. [tex]$1 J=1 kg \cdot m ^2 / s ^2$[/tex]
Thus, the answer to the question is option A.
