What does the unit N/m represent?

The unit N/m, which stands for Newton per meter, represents a measure of force per unit length. To understand why the correct answer is kg/s², it's essential to first break down what a Newton (N) is in terms of its base SI units.

A Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared. Thus, in base units, 1 N = 1 kg·m/s².

When we look at the unit N/m, we can substitute the definition of the Newton into this expression:

N/m = (kg·m/s²) / m

Upon simplifying this, the meters in the numerator and denominator cancel out, leading us to:

N/m = kg/s²

This result shows that N/m is indeed a measure of force divided by length, which correlates to acceleration (force per unit mass) in contexts such as stiffness in mechanics.

The other answer choices do not represent this relationship accurately:

• kg * m represents mass times length, which does not relate to the concept of force or acceleration.
• kg/s corresponds to mass per unit time, indicating a flow or rate of mass, unrelated to force or distance.
• kg *