Give the derived SI units for each of the following quantities in base SI units: (e) power = work/time

Verified step by step guidance

1. Understand that power is defined as the rate at which work is done, or work divided by time.
2. Recall that work is defined as force times distance. In SI units, force is measured in newtons (N) and distance in meters (m). Therefore, work has units of newton-meters (N·m), which is equivalent to joules (J).
3. Recognize that time is measured in seconds (s) in SI units.
4. Combine these to express power in terms of base SI units: Power = Work/Time = Joules/Seconds.
5. Since 1 Joule is equivalent to 1 kg·m²/s², the derived SI unit for power is kg·m²/s³, which is also known as a watt (W).

Key Concepts

SI Units

The International System of Units (SI) is a standardized system of measurement used globally in science and engineering. It is based on seven base units, including the meter for length, kilogram for mass, and second for time. Derived units are formed from these base units to measure other quantities, such as power, which is derived from work and time.

Work

In physics, work is defined as the energy transferred when a force is applied to an object over a distance. The SI unit of work is the joule (J), which is equivalent to one newton-meter (N·m). Understanding work is essential for calculating power, as power is the rate at which work is done.

Power

Power is the rate at which work is performed or energy is transferred over time. The SI unit of power is the watt (W), which is defined as one joule per second (J/s). This relationship highlights how power quantifies the efficiency of energy use, making it a crucial concept in various scientific and engineering applications.