Question

How can Newton’s first law of motion be obtained from the second law of motion?
A. When net force is zero
B. When net force is positive
C. When moving with constant speed
D. When velocity is zero

Answer 1

This question has multiple correct options. Recall Newton’s first and second law of motion. According to Newton’s second law of motion, if the net force acting on the body is zero, the acceleration of the body is zero. The zero acceleration implies uniform motion of the body.

Complete step by step solution:
and until it is acted by an external force to halt its motion or change the direction. Also, the body in the rest position remains in the rest position if it is acted by an external force to accelerate.
Newton’s second law of motion states that if any force acts on the body, it produces acceleration in that body. The force acting on the body is the product of its mass and acceleration. Therefore,$F = ma$, where, m is the mass and a is the acceleration.
Now, we consider the first case when the net force is zero. Then,
$0 = ma$
$\Rightarrow a = 0$
We have, $a = \dfrac{{{v_f} - {v_i}}}{t} = 0$
$\Rightarrow {v_f} = {v_i}$
Here, ${v_f}$ is the final velocity and ${v_i}$ is the initial velocity.
We can see that the velocity of the body does not change if the acceleration is zero. Therefore, the body is in its state of uniform motion when there is absence of net force. This follows Newton’s first law. So, the option (A) seems to be correct answer.
When net force is positive, the body has non zero acceleration. The body with acceleration cannot be said to be in uniform motion as its speed changes at every second. Therefore, the option (B) is incorrect.
Now, we consider the third case when the velocity of the body is constant. We have discussed above that the acceleration of the body is given as,
$a = \dfrac{{{v_f} - {v_i}}}{t}$
Since the velocity of the body does not change, we can write,
$a = \dfrac{{{v_i} - {v_i}}}{t}$
$\Rightarrow a = 0$
Therefore, from Newton’s second law, $F = ma$, we can say that the net force to change the motion of the body is zero. Thus, the body remains in its uniform motion which is the condition for Newton’s first law. So, the option (C) seems to be the correct answer.
Now, we consider the fourth case when the velocity of the body is zero. In that case, the body is not moving. This implies that the net force on the body is zero. We know from Newton’s first law, the body will remain in its state of rest unless and until it is acted upon by the external force. Therefore, the option (D) also seems to be the correct answer.

So, the correct answer is option (A), (C), and (D).

Note:
While considering the motion of the body, you should consider all the forces acting on the body. The summation of all the forces with direction is the net force. If the net force is zero, then and then only the body has zero acceleration.