Question

derive the formula F = MA , WHERE F = FORCE , M = MASS , A = AECCELRATION

Answer 1

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Answer 2

Answer:

Explanation:

Derivation :-

Let m be the mass of the body.

And its initial velocity is u.

Initial momentum, P₁ = mu .... (i)

After applying a constant force, F on this body

Accelerated to a velocity, v to time t

Then,

Mass of the body = m

Final velocity, = v

Final Momentum, P₂ = mv .... (ii)

Change in momentum = Final Momentum - Initial Momentum

Change in momentum = P₂ - P₁ .... (iii)

Now, According to 2nd law of motion,

F ∝ Change in momentum/Time taken

F ∝ P₂ - P₁/t    [From Eq (iii)

F ∝ mv - mu/t   [From Eq (i) and (ii)}

F ∝ m(v - u)t

F ∝ m(v - u/t)    [From a = v - u/t]

F ∝ ma

F ∝ Ka    [Where k is constant]

The value of K in SI unit is 1.

F = ma

Hence, Derived.