# Reason for motion after terminal velocity

Let some object hang by a string. So no motion since weight was counter balanced no net force. Now string is cut. Object is falling under gravity and experiences air resistance. Terminal velocity is reached when weight is equal to the air resistance. So no net force and no net acceleration after terminal velocity. But why does the object continue to fall if there is no net force acting on it, why doesnt it just hang in mid air dead stopped ?

• "Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it" - some guy or other. That's a net force, if there are two equal and opposite forces, they cancel out. Jan 11 '15 at 0:40
• Its look like a common misconception. remember a body can be in uniform linear motion without any help of external force.
– Paul
Jan 11 '15 at 1:46
• Your logic is correct. But it does not stop because terminal velocity is not 0 ! So the medium could not bring the object to halt (like in the case of string), it could only bring it to "equilibrium". Imagine that the object will start stopping in midair, but then it will have no air resistance! :) And hence there will be no terminal velocity "effect" to compensate for the weight. Jan 11 '15 at 2:11

In order to change the velocity of the object from falling ($v=v_{terminal}$) to stopped ($v=0$), then it would have to decelerate.

You mention in your question that the net force is zero and there is no acceleration. Since there is no acceleration, the velocity must remain the same.

The object is accelerating until drag equals gravity. At that point, it stops accelerating and maintains the velocity it has.

According to newtons law an object continues to move in a straight line or remains at rest unless or until some unbalanced force acts on it. In your case when terminal velocity is reached at that time the object had velocity and no net force acts on it so it continues to move and rather not stop. To stop its motion you need to apply some force again ex frictional force which stops an object.

• Hi, thanks for all the rewarding thoughts. If its moving because of inertia (no net force) and if it falls distance x at terminal velocity then whats the work done in terms of -- Work = Force x Displacement. Jan 13 '15 at 22:52

The object is moving with the terminal velocity, which points downward. Hence, the object will continue to fall.

• This doesnt ans the question explicitly.
– Paul
Jan 11 '15 at 1:43

Let

$$v^2=u^2+2as$$

At some point $$a=0 \ \mathrm ms^{-2}$$ which means the object isn't accelerating anymore. So,

$$v=u$$

At the last moment of where the acceleration goes to $$0$$ there velocity is "something". Velocity isn't constant. Hence the object keeps falling. The object is keep falling until the velocity is $$0\ \mathrm ms^{-2}$$.