An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, then state the conditions that must be placed on the magnitude and direction of the velocity. If no, provide a reason.

Hint: According to Newton’s first law of motion an object will change its state only when the net force acting on it is non-zero. Therefore, when a net non zero force will act on an object then the velocity of that object is changed (either magnitude or direction). When net external force is zero, the object will continue its motion, if it is at rest then it will remain at rest and if it is moving with some uniform velocity then it will continue that motion in the same velocity and in the same direction.

Complete step-by-step answer:
According to Newton’s first law of motion, every object continues its state of rest or state of uniform motion unless and until an external unbalanced force acts on it.
Therefore, when net \[F=0\], then change in v=0
According to Newton’s second law of motion, force F is the product of mass m and acceleration of an object a.
Thus, \[F=ma\]
Here, acceleration a is given as
$a=\dfrac{{{v}_{f}}-{{v}_{i}}}{t}$
Where,
 ${{v}_{i}}$ is the initial velocity of the object and
${{v}_{f}}$ is the final velocity of the object
Now, when F=0, ma=0 and thus a=0
Therefore,
$\begin{align}
  & a=\dfrac{{{v}_{f}}-{{v}_{i}}}{t}=0 \\
 & \Rightarrow {{v}_{f}}={{v}_{i}} \\
\end{align}$
Thus, if an object was moving with some uniform initial velocity then it would continue its motion with the same velocity with no change in direction even when it is acted by a net unbalanced force which is zero.
Therefore, when an object experiences a net zero external unbalanced force, it is possible for the object to be travelling with a non-zero velocity.

Note: If a balanced force is acting on an object then it will not change the velocity or position of the object, it will change only its shape and size of that object. Imagine a scenario when you push the wall, we feel that we are applying an unbalanced force but still, the wall is not changing its position. In this case, the force which we are applying is balanced by the internal forces of the wall. Therefore, an object will not change its velocity or position as long as the external forces are balanced by the inertial or internal forces of the object.