Question

If the net external force acting on a body is zero
(A) It must be in the state of rest
(B) It must be moving with constant speed
(C) It must be moving with constant velocity
(D) Either at rest or moving with constant velocity

Answer 1

Hint
Newton’s second law of motion is used to solve this problem. The formula for force given by Newton’s second law of motion gives us the state of motion at which a body is (if the body is at rest or motion). The net external force is zero, so either mass or acceleration is zero. Since mass cannot be zero, different possibilities for acceleration equal to zero are analyzed. Velocities in each of these cases are noted and checked to find which of the options is true.
$F = ma$, Newton’s second law of motion is used to solve this problem
Here, $F,m,a$ represent force, mass, acceleration respectively.

Complete step by step answer
Newton’s second law of motion states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force.
The formula for the external force applied on a body is given as a product of mass and acceleration. From the question, we know that the net external force acting on the body is zero. This means that either mass or acceleration has to be zero. Since mass cannot be zero, it has to be an acceleration that is zero.
Acceleration is the change in velocity with respect to time. This tells us that acceleration can be zero in two cases,$a = \dfrac{{v - u}}{t}$
-When both final and initial velocities are zero. ($v = 0,u = 0$)
-When initial and final velocities equal but greater and zero. ($v = u$)
In the first case, the acceleration of the body is zero because the velocity is zero. This means the body is at rest.
In the second case, the acceleration of the body is zero but the velocity is not zero. This means the body is in motion with constant velocity.
Hence when the external force is zero, the body can either be in a state of rest or in motion with constant velocity.
Thus, the correct answer is Option (D) Either at rest or moving with constant velocity.

Note
Remember that speed and velocity are two different qualities. Acceleration is the change of velocities with respect to time which is why velocity is considered for finding acceleration which then gets us the force. Speed and velocity are equal only when the distance traveled by the body is equal to the displacement of the body. This is true only when the body is traveling in a straight line.