Question

What is Newton’s second law of motion? Define it. Obtain Newton’s first law from it.

Answer 1

Hint:Our knowledge related to Newton's laws of motion are very crucial in order to relate both the laws, Newton’s First Law of motion and Newton’s Second Law of Motion. Using the equation of Second law and equation of motion in correct order and mathematically correct we can find relation between both laws. We must clearly know what these laws read and state.

Formula Used:
$F = ma$
$\Rightarrow v - u = at$
Here, $m$ = mass of the body, $a$= acceleration of the body, $v$= final velocity, $u$= initial velocity and $t$= time.

Complete step by step answer:
Newton’s first law of motion states that, every object/body will remain constant in its state of motion until or unless an external force is applied on it i.e. a body if initially is at place of rest will remain at rest until force is applied on it and will keep moving with constant velocity until a force is applicable on it.

According to Newton’s second law of motion,any change in rate of momentum in the motion of body is directly related to force applied on that body and always takes place in direction in which force is applied i.e.
$F \propto \dfrac{{\vartriangle p}}{{\vartriangle t}}$
$F$ is the force applied depicting the direct effect on $\dfrac{{\vartriangle p}}{{\vartriangle t}}$ which is the rate of change in momentum.

This law can also be expressed in terms of acceleration and mass (by resolving the rate of change of momentum) as,
$F = ma$
Where, $F = f{\text{force applied}}$
$m = {\text{mass of body}}$
$a = {\text{acceleration produced in body on application of force F}}$
In terms of mass and acceleration we can state that, according to the second law of motion, acceleration of a body is directly dependent upon force applied and inversely to mass contained in the body.

Comparing both laws: Assume a body is moving at a constant speed $u$. If no force will be acting on body then,
$F = ma = 0$
So acceleration in the body will be zero as no force is acting on body. . ……….. (Newton’s second law)
Now according to equation,
$v - u = at$
Where, $v = {\text{final velocity of body}}$
As acceleration is zero because no force is acting on body hence,
$v - u = 0 \times t$
$\therefore v = u$ ……$(i)$
The above equation $(i)$ clearly shows that there is no change in velocity of the body (i.e. it keeps moving with same velocity on removal of force. …………….. (Newton’s first law)

Note:It is very important to remember that both laws are dependent on force and explain the effect of force on the motion of the body. Every law is derivative of each other and has a great impact on the physics of daily life. We must be very clear in our mind about all laws of motion as these are the foundation of most of the fields and branches of physics.