According to Newton's 2nd law of motion, F=k(m)(a), where k= constant. Now when F=1,m=1,a=1, then k=1. But when F,m,a each≠1 then the formula is not valid. So how can we say that F=(m)(a) is true everywhere in every case.We also solve questions by taking this formula only.
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I'm not sure where your confusion lies. According to Newton's second law of motion, the rate of change of momentum is directly proportional to the force applied.
$$\vec{F} \propto \frac{d \vec{p}}{dt}$$
If the mass of the system remains constant
$$\vec{F} \propto m \frac{d \vec{v}}{dt}$$
Or we can write it as
$$\vec{F} = k m \vec{a}$$
where $k$ is a constant of proportionality.
We define a unit force as a force which can produce a unit acceleration in a body of unit mass. Using $k = 1$, we get the familiar equation
$$\vec{F} = m \vec{a}$$
Mechanic
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k the constant of proportionality is ALWAYS taken to be 1 because force is directly proportional to acceleration.
If we use your equation F = kma. This can be seen by graphing force you dependent variable against acceleration you independent variable. The gradient k, passes though the origin with a gradient of 1 due to it's direct proportionality.
(The gradient is k because mass is a constant)
Therefore, 1 (the gradient of your line) = k when this occurs this is called a linear relationship.
Hope this helps.
Callum
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