Question

state Newton's second law of motion hence derive the equation of motion f=ma from it​

Answer 1

Answer:

Newton's second law states that the rate of change of momentum of a body is directly proportional to the external force acting on the body

From Newton's second law, F∝dp/dt

               F=kdp/dt

               k=1

               F=dp/dt

               F=d(mv)/dt

               F=m x dv/dt  (dv/dt=a)

              F=ma

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Answer 2

$\huge{\mathfrak{Bonjour!♡}}$⭑°•⭑

${\underline{\underline{\textbf{NeWton's Second Law Of Motion:-}}}}$

Statement:-

★Force acting on an object is directly proportional to the rate of change of its momentum with respect to time. It takes place in the direction in which the force acts.

Derivation:-

$\sf{F=\frac{ Mv-Mu}{t}}$

$\leadsto \: { \tt{F= \frac{m(v - u)}{t} }} \\ \\ \leadsto \: { \bf{F \: = ma}} \: \: \: { \sf{(a = \frac{v - u}{t} )}}$

$\sf{Where}\begin{cases}\sf{F= Force}\\ \ \sf{m=mass}\\ \ \sf{a=acceleration}\\ \ \sf{v= final\: velocity}\\ \ \sf{u= intial\: velocity}\\ \ \sf{t=time}\end{cases}$

Derivation by Calculus Method:-

According to statement the force is directly proportional to the rate of change of momentum. So,

F = kdp/dt (p= momentum)

F= dp/dt (k= constant=1)

F= dmv/dt (p=mv)

F= mdv/dt

$\bf{F= ma}$

Unit:-

•Newton or kgm/sec²

• Dyne(CGS unit)

• 1 N = 10^5 dyne

Examples:-

• Cricket player increases time to reduce force or momentum.

• Karate player reduce time to increase force.