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My book says that according to first law force applied is proportional to mass times acceleration is $$F=kma.$$ Now it says that for convenience we take $k=1$ and it does not affect anything. But my question is if we take any other value of $k$,equations of kinetic energy, motions of equation etc would change? how can we take $k=1$ conveniently. EDIT-Previous answers say that k=1 because force is defined so that it is "easy" to remember. Therefore my new question is if we define F=2Ma and then derive new results for kinetic energy etc,will they be valid too?

Polario
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  • Possible duplicates: https://physics.stackexchange.com/q/104101/2451 and links therein. – Qmechanic May 26 '18 at 19:17
  • @qmechanic please see if my new question still comes under the above link. – Polario May 26 '18 at 19:22
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    If you so wished, you could define the unit of force as 196133/6096 times the unit of mass times the unit of acceleration, the unit of power as 1/550 times the unit of length times the unit of force, and all kinds of other craziness. Everything will work just fine -- so long as you remember to carry all those different proportionality factors. Except it's crazy. There's only one major country in the world that indulges in this craziness. – David Hammen May 26 '18 at 23:05

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