Prove that F = ma.


F = ma is the formula of Newton’s Second Law of Motion.

Newton’s Second Law of Motion is defined as Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.

Newton’s second law

The second law of Newton can be described simply as the acceleration of an entity as produced by a net force is directly proportional to the magnitude of the net force, in the same path as the net force, and inversely proportional to the mass of the entity.

Proof for F=ma

Let us consider an object of mass m, moving along a straight line with an initial velocity u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v. Here we see that, the initial momentum

p1 = m × u

The final momentum

p2 = m × v

The change in momentum can be expressed as

p2 – p1 = (m × v) – (m × u)

p2 – p1 = m (v – u)

But we know that the rate of change of momentum with respect to time is proportional to the applied force.

The applied force

F ∝ [m (v – u)]/t

F ∝ m × a

as acceleration (a) = rate of change of velocity with respect to time.

F = k × m × a

Check out the video given below to know more about motion

Further Reading

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