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Wize AP Physics C: Mechanics Textbook > Unit 2: Newton's Laws of Motion (17-23%)

Resistive Force and Terminal Velocity

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Terminal Velocity


  • Say, a body is freely falling in a vacuum. Then the force acting on it F=mg.
  • In presence of air or other fluids, it will experience a drag force (resistive force due to fluid) against its motion.
  • This resistive force is usually increasing with the speed of the object
  • On some cases it may happen that the drag force will become equal to the force of gravity. Hence the body will experience no net force; hence it will fall with a constant velocity, known as the terminal velocity.




Exam Tip
Terminal velocity could be found by making gravitational force and drag force equal to each other! (You might need to consider other forces as well if there are more forces exerting on the object)

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Resistive Force

The resistive force is typically described by the equation:

Fr⃗=−kv⃗\boxed{\vec{F_r} = -k\vec{v}}

  • Where "k" is a constant
  • Using Newton's 2nd Law the Net Force: ∑F⃗=F⃗Net=ma⃗\sum\vec{F} = \vec{F}_{Net} = m\vec{a}
  • Setting Fr to equal ma we obtain:
ma⃗=−kv⃗m\vec{a} = -k\vec{v}
  • Acceleration is the time derivative of velocity, so we can obtain the differential form of the resistive force
mdv⃗dt=−kv⃗\boxed{m\frac{\vec{dv}}{dt}=-k\vec{v}}