Derive the fundamental SI units of power using the definitions of power, work, force, and acceleration.

Power ($P$) is the rate at which work ($W$) is done or energy is transferred over time ($t$).

Work ($W$) is the product of force ($F$) and displacement ($d$).

Substitute this into the power equation:

Force ($F$) is the product of mass ($m$) and acceleration ($a$).

Substitute this into the power equation:

• Mass ($m$): $\text{kg}$
• Acceleration ($a$): $\text{m/s}^2$ (since acceleration is change in velocity over time, and velocity is change in displacement over time, $a = \frac{\text{m/s}}{\text{s}} = \text{m/s}^2$)
• Displacement ($d$): $\text{m}$
• Time ($t$): $\text{s}$

Thus, the fundamental units of power are $\text{kg m}^2/\text{s}^3$.