Give the derived SI units for each of the following...

Give the derived SI units for each of the following quantities in base SI units: (a) acceleration = distance/time $^{2}$ (b) force $=$ mass $\times$ acceleration (c) work $=$ force $\times$ distance (d) pressure = force/area (e) power = work/time (f) velocity $=$ distance/time (g) energy $=$ mass $\times(\text { velocity })^{2}$

Give the derived SI units for each of the following quantities in base SI units:
(a) acceleration = distance/time $^{2}$
(b) force $=$ mass $\times$ acceleration
(c) work $=$ force $\times$ distance
(d) pressure = force/area
(e) power = work/time
(f) velocity $=$ distance/time
(g) energy $=$ mass $\times(\text { velocity })^{2}$

Key Concepts

Power

Power is the rate at which work is performed or energy is transferred over time. Its SI unit is the Watt (W), where 1 W is equivalent to 1 Joule per second (J/s), expressed as 1 kg·m²/s³.

Pressure

Pressure is defined as the force distributed over a unit area. The SI derived unit for pressure is the Pascal (Pa), where 1 Pa equals 1 N/m² or equivalently 1 kg/(m·s²).

Work and Energy

Work and Energy both involve the application of force over a distance. The SI unit for work and energy is the Joule (J), defined as the work done when a force of one Newton moves an object one meter, equivalent to 1 kg·m²/s².

Velocity

Velocity is a vector quantity that measures the rate of change of displacement over time. The SI unit for velocity is meters per second (m/s).

Acceleration

Acceleration represents the rate of change of velocity over time and is defined as distance divided by time squared. In SI units, it is expressed as meters per second squared (m/s²).

Derived SI Units

Derived SI Units are units that are derived from the base SI units by combining them according to the physical relationships between different quantities. They allow complex physical concepts like force, work, and power to be expressed in terms of the base units.

SI Base Units

SI Base Units are the fundamental units of measurement defined by the International System of Units for quantities such as length (meter), mass (kilogram), and time (second). These form the foundation for expressing all other measurements in science.

Force

Force is the interaction that causes an object to change its state of motion, defined as mass multiplied by acceleration. Its SI derived unit is the Newton (N), where 1 N is equivalent to 1 kg·m/s².

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