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Some important and basic points:
Unit of time is second (s).
Unit of mass is kilogram (kg).
Unit of distance/displacement is meter (m).
P.S. Displacement and distance are nearly same things, their unit is same.
Speed/velocity = distance/time
So, its unit is m/s.
Acceleration = (final velocity-initial velocity)/time.
So, its unit is m/s² or m.s^-2
We know from the formula that,
Force = mass × acceleration
=> F = ma
Putting units:
Newton = kg.m/s² or kg.m.s^-2 _____(1)
Putting dimensions:
Newton = M.L.T^-2
________________________
We know from the formula that,
Work = force × displacement
=> W = Fs
Putting units:
Joule = Newton.m
=> Joule = kg.m.s^-2.m [from (1)]
=> Joule = kg.m².s^-2 ______(2)
Putting dimensions:
Joule = M.L².T^-2
________________________
We know from the formula that,
Power = work/time
Putting units:
Watt = joule/s
=> Watt = kg.m².s^-2/s [from (2)]
=> Watt = kg.m².s^-3 ______(3)
Putting dimensions:
Watt = M.L².T^-3
________________________
We know from the formula that,
Horsepower = 746 watt
=> Horsepower = 746kg.m².s^-3 [from (3)]
Putting dimensions:
Horsepower = 746M.L².T^-3
The dimension of Watt, Newton and horsepower are ML²T⁻³, MLT⁻² and ML²T⁻³ respectively
Units are measure of a quantity. Dimensions are derived from the units. Gi
Force = mass × acceleration
For Newton:
Another representation for unit of Newton is kg.m/s². Writing in terms of the dimension
Newton = MLT⁻²
For Watts;
The unit of Watt is also kg.m².s⁻²/s which is equivalent to kg.m².s⁻³
In terms of dimension
Dimension of Watt = ML²T⁻³
For Horse power:
The unit of horse power is kg.m².s⁻³
Dimension of horsepower = ML²T⁻³
Learn more on units and dimension here: https://brainly.com/question/28464
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