Explain how the basic unit are combined to give the derived units of force, velocity, pressure and work

Velocity:

Velocity is change in displacement with respect to time:

Analysing the units, meters (displacement) and seconds (time) are basic units:

Therefore the unit of velocity is m/s

Force:

Newton's second law of motion:

Kilogram (mass) is a basic unit, and accelerations unit can be found using the equation:

Analysing the units:

Therefore, the unit of force is:

Pressure:

Pressure is given by the equation:

where S is area of effect, F is force

Area for a basic rectangle (geometric shape is arbitrary for dimensional analysis) is found by multiplying two lengths:

, the unit of area

Dividing the aforementioned unit of force by the unit of area:

, the unit of pressure

Work:

Work is given by the equation:

, (dot product may be assumed as normal multiplication for the purposes of unit analysis)

Knowing displacement's (x) unit is m:

, the unit of work.

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