Velocity:
Velocity is change in displacement with respect to time:
[tex]\frac{\Delta x}{\Delta t}[/tex]
Analysing the units, meters (displacement) and seconds (time) are basic units:
[tex]\frac{m}{s}[/tex]
Therefore the unit of velocity is m/s
Force:
Newton's second law of motion:
[tex]F = ma[/tex]
Kilogram (mass) is a basic unit, and accelerations unit can be found using the equation:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
Analysing the units:
[tex]\frac{\frac{m}{s}}{s}=\frac{m}{s^2}[/tex]
Therefore, the unit of force is:
[tex]kg\frac{m}{s^2}[/tex]
Pressure:
Pressure is given by the equation:
[tex]P=\frac{F}{S}[/tex] 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:
[tex][l^2]=m^2[/tex], the unit of area
Dividing the aforementioned unit of force by the unit of area:
[tex]\frac{kg\frac{m}{s^2}}{m^2}=\frac{kg}{ms^2}[/tex], the unit of pressure
Work:
Work is given by the equation:
[tex]W=\vec{F}\cdot \vec{x}[/tex], (dot product may be assumed as normal multiplication for the purposes of unit analysis)
Knowing displacement's (x) unit is m:
[tex][W]=\frac{kgm}{s^2}m=\frac{kgm^2}{s^2}[/tex], the unit of work.
