State Newton's second law of motion and shown that the first law of motion can be mathematically started from the Newton's seconds law.

Answer:

Newton’s second law of motion can be stated as the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Newton’s Second Law

The Newton second law is mainly based on the two terms of physics that is force and acceleration.

Newton’s second law can be formally stated as

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. The acceleration of the body that is acting is directly proportional to force and is inversely proportional to the mass of the body. Hence when the force acting on a body is increased, the acceleration increases. Similarly, when the mass of the body is increased, the acceleration decreases.

This statement is expressed in equation form as,

\(\begin{array}{l}a=\frac{F_{net}}{m}\end{array} \)

The above equation can be rearranged to a familiar form as

F = ma

Since force is a vector, Newton’s second law can be written as

\(\begin{array}{l}\vec{F}=m\vec{a}\end{array} \)

Get a glimpse of Newton’s second law of motion being taught in BYJU’S classes.

First law of motion can be started from the Newton’s seconds law

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 is

p2 – p1 = (m × v) – (m × u)

p2 – p1 = m (v – u)

The rate of change of momentum with respect to time is proportional to the applied force. The applied force is

F ∝ m (v – u)/t

or

F ∝ m × a

a = Rate of change of velocity/Time

F = k × m × a

k = proportionality constant.

Hence from the second law of motion, we get force is the product of mass and acceleration i.e F = ma.

Check out the video given below to know more about motion

Further Reading:

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