Question

Derive the Newton's third equation motion explain with diagram.​

Answer 1

Answer:

Derivation of Second Equation of Motion by Graphical Method

Taking the same diagram used in first law derivation:

Derivation Of Equation Of Motion

In this diagram, the distance travelled (S) = Area of figure OABC = Area of rectangle OADC + Area of triangle ABD.

Now, the area of the rectangle OADC = OA × OC = ut

And, Area of triangle ABD = (1/2) × Area of rectangle AEBD = (1/2) at2 (Since, AD = t and BD = at)

Thus, the total distance covered will be:

S = ut + (1/2) at2

Derivation of Second Equation of Motion by Calculus Method

Velocity is the rate of change of displacement.

Mathematically, this is expressed as

v=dsdt

Rearranging the equation, we get

ds=vdt

Substituting the first equation of motion in the above equation, we get

ds=(u+at)dt =(udt+atdt) ∫s0ds=∫t0udt+∫t0atdt s=ut+12at2

Derivation of Third Equation of Motion

The third equation of motion is:

v2 = u2 + 2aS

Derivation of Third Equation of Motion by Algebraic Method

Derivation Of Third Equation Of Motion

Derivation of Third Equation of Motion by Graphical Method

Derivation Of Equation Of Motion

The total distance travelled, S = Area of trapezium OABC.

So, S= 1/2(SumofParallelSides)×Height

S=(OA+CB)×OC

Since, OA = u, CB = v, and OC = t

The above equation becomes

S= 1/2(u+v)×t

Now, since t = (v – u)/ a

The above equation can be written as:

S= 1/2(u+v)×(v-u)/a

Rearranging the equation, we get

S= 1/2(v+u)×(v-u)/a

S = (v2-u2)/2a

Third equation of motion is obtained by solving the above equation:

v2 = u2+2aS

Derivation of Third Equation of Motion by Calculus Method

It is known that,

Derivation Of Equation Of Motion

These were the detailed derivations for equations of motion in the graphical method, algebraic method and calculus method.

Equations of Motion Formula

Equations of motion Formula

First equation of motion v=u+at

Second equation of motion s=ut+12at2

Third equation of motion v2 = u2+2as

Answer 2

Explanation:

Newtons 3rd Law.≈ state that for every action(force) in nature there is a equal and opposite reaction.

in other words if objects A exerts a force on object B also exerts an a opposite force of Objects A.

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