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Motion in the Presence of Resistive Forces in Physics

Air and water push back, and the harder they are pushed the harder they push. That single feedback loop is what separates this topic from ordinary constant-acceleration motion, because the acceleration keeps shrinking as the speed grows until it disappears altogether. The speed it settles at is the terminal speed, and it depends on whether the resistance grows in proportion to the speed or in proportion to the square of the speed. The blocks cover both models, the terminal speed each one predicts, and how the speed and the distance evolve while the body is still approaching that limit.

Resistive force proportional to the speed

Given

  • (kg/s)
  • (m/s)
Acceleration when the resistance is proportional to the speed

Given

  • (kg/s)
  • (kg)
  • (m/s)

Constant used

Terminal speed when the resistance is proportional to the speed

Given

  • (kg)
  • (kg/s)

Constant used

Time constant of a motion resisted in proportion to the speed

Given

  • (kg)
  • (kg/s)
Speed as a function of time with resistance proportional to the speed

Given

  • (m/s)
  • (s)
  • (s)

Constant used

Distance fallen as a function of time with resistance proportional to the speed

Given

  • (m/s)
  • (s)
  • (s)

Constant used

Resistive force proportional to the square of the speed

Given

  • (kg/m³)
  • (m²)
  • (m/s)
Acceleration when the resistance is proportional to the square of the speed

Given

  • (kg)
  • (m/s)

Constant used

Terminal speed when the resistance is proportional to the square of the speed

Given

  • (kg)

Constant used

Terminal speed when the resistance is written as b times the square of the speed

Given

  • (kg)
  • (kg/m)

Constant used

Speed as a function of time with resistance proportional to the square of the speed

Given

  • (m/s)
  • (s)

Constants used

Distance fallen as a function of time with resistance proportional to the square of the speed

Given

  • (m/s)
  • (s)

Constants used