Certainly! Let's analyze the given options to determine which one correctly describes force using SI units:
First, recall the fundamental relationship that defines force in physics:
[tex]\[ F = m \times a \][/tex]
where [tex]\( F \)[/tex] is the force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration.
The SI unit of force is the Newton (N), the SI unit of mass is the kilogram (kg), and the SI unit of acceleration is meters per second squared ([tex]\( m/s^2 \)[/tex]).
Therefore, the relationship in SI units is:
[tex]\[ 1 \, \text{Newton} (N) = 1 \, \text{kg} \times 1 \, m/s^2 \][/tex]
So, let's assess each option:
A. [tex]\( 1 \, N = 1 \, kg \cdot m / s^2 \)[/tex]
This matches our equation [tex]\( F = m \times a \)[/tex], where [tex]\( a \)[/tex] (acceleration) is in [tex]\( m/s^2 \)[/tex]. Therefore, this is correct.
B. [tex]\( 1 \, N = 1 \, kg \cdot m / s \)[/tex]
This suggests force equals mass times velocity, but the proper relation uses acceleration ([tex]\( m/s^2 \)[/tex]), not velocity ([tex]\( m/s \)[/tex]). Thus, this is incorrect.
C. [tex]\( 1 \, J = 1 \, kg \cdot m / s^2 \)[/tex]
This states Joules (J), unit of energy, which isn't related to the unit of force (Newton). Therefore, this is incorrect.
D. [tex]\( 1 \, J = 1 \, kg \cdot m / s \)[/tex]
Again, this confuses energy (Joule) with an incorrect corresponding unit of force. Therefore, this is incorrect.
Thus, the only correct expression that describes force using SI units is:
[tex]\[ \boxed{1 \, N = 1 \, kg \cdot m / s^2} \][/tex]
So, the correct choice is:
A. [tex]\( 1 \, N = 1 \, kg \cdot m / s^2 \)[/tex]
