Chapter 8, Problem 54A

Using units, show that $\text{kg}\cdot \text{m/s}$ is equivalent to $\text{N}\cdot \text{s}$.

To determine

To Prove: The unit $\text{kg}\cdot \frac{\text{m}}{\text{s}}$ is equivalent to the $\text{N}\cdot \text{s}$ .

Explanation of Solution

Introduction:

Newton is the unit of force which is equal to $\text{kg}\cdot \frac{\text{m}}{{\text{s}}^2}$ and force is the product of mass and acceleration.

Newton is the unit of force, which is given as,

  $\text{N=kg}\cdot \frac{\text{m}}{{\text{s}}^2}$

Multiplying with ‘s’ both sides:

  $\begin{array}{l}\text{N}\cdot \text{s = kg}\frac{\text{m}}{{\text{s}}^{\text{2}}}\text{×s}\\ \text{N}\cdot \text{s}\text{=}\text{kg}\frac{\text{m}}{\text{s}}\end{array}$

Hence, both are the same units.

Conclusion:

Hence, $\text{kg}\frac{\text{m}}{\text{s}}$ is equivalent to the $\text{N}\cdot \text{s}$ .