Question

derive the mathematical form of force
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Answer 1

Answer:

force applied directly proportional to the product of mass and acceleration. unit of force is given by the unit of mass and acceleration force is directly proportional when initial and final condition.

Answer 2

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Newton’s Second Law

The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.

A vector equation is the modern statement of newton’s second law:

${\rm{{\vec{F}} = \frac{\vec{dp}}{dt}}}$

Where

${\rm{\vec{p} = momentum \: and}} \\ {\rm{ \vec{p} = mv}}</p><p>$

If the time interval for the applied force increases, as a result, the value of the force applied decreases.

From newton’s second law of motion:

${\rm{\vec{F}\alpha\frac{ \vec{dp}}{dt}}} \\ {\rm{\vec{F} = K \times \frac{\vec{dp}}{dt} = \vec{kma}}}$

For simplicity, the constant of proportionality (k) is decided to be 1, therefore:

${\boxed{\rm{\vec{F}= \vec{ma}}}}</p><p></p><p>$

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