Represent each of the following units as a combination of primitive dimensions where M=mass, L=length, T=time

PLS show work

Watt

Newton

Horsepower

Force = mass × acceleration

=> F = ma

Putting units:

Newton = kg.m/s² or kg.m.s^-2 (1)

Work = force × displacement

=> W = Fs

Putting units:

Joule = Newton.m

=> Joule = kg.m.s^-2.m [from (1)]

=> Joule = kg.m².s^-2 (2)

Power = work/time

Putting units:

Watt = joule/s

=> Watt = kg.m².s^-2/s [from (2)]

=> Watt = kg.m².s^-3

Explanation:

Watt and Horsepower are both units for power; which is defined as Energy / Time.

Energy is defined as Force * Distance.

Newton is a unit of Force.

Force is equal to mass * acceleration and acceleration is Distance / Time^2

So Newton = mass * (length / time^2)

= ML/T^2

Watt and Horsepower = Force * L / T

= ML^2/T^3

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