Terminal velocity

Forces in Action - OCR A-Level Physics

Key Definition
Terminal velocity
The constant velocity reached when the drag force on a falling object equals its weight, so the resultant force and acceleration are zero.
  • When an object first starts falling, weight > drag, so it accelerates downwards
  • As speed increases, drag increases (drag is speed-dependent)
  • Eventually drag = weight: resultant force = 0, $accelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantity. Measured in m s⁻². = 0. The object moves$ at terminal velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.The constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. reached when the driving force on an object is exactly balanced by resistive forces, so the resultant force is zero.
  • A parachutist reaches terminal velocityThe constant velocity reached when the driving force on an object is exactly balanced by resistive forces, so the resultant force is zero. twice: once in free fallMotion under gravity alone, with no other forces acting. All objects in free fall near Earth's surface have the same acceleration, g = 9.81 m s⁻². (~55 $m s^{-1}$) and again after the parachute opens (~5 $m s^{-1}$)
  • Opening the parachute increases the surface area, which increases drag. The parachutist decelerates until a new, lower terminal velocityThe constant velocity reached when the driving force on an object is exactly balanced by resistive forces, so the resultant force is zero. is reached
Worked Example [4 marks]
Describe and explain the shape of the velocity-time graph for a parachutist who jumps from a plane and later opens a parachute.
Show Solution
1

Initially, velocity increases rapidly because weight >> drag, giving a large downward resultant force and large accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻².

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2

As speed increases, drag increases, so the resultant force decreases and the rate of accelerationThe rate of change of velocity. A vector quantity. Measured in m s⁻². decreases (the graph curves, becoming less steep)

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3

Terminal velocityThe constant velocity reached when the driving force on an object is exactly balanced by resistive forces, so the resultant force is zero. is reached when $drag = weight$; the graph becomes horizontal (constant velocity)

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4

When the parachute opens, drag suddenly exceeds weight (increased surface area). The parachutist decelerates to a new, lower terminal velocity where drag once again equals weight

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Answer
The graph shows increasing velocity with decreasing gradient, levelling off at terminal velocity, then a sudden decrease when the parachute opens, levelling off again at a lower terminal velocity.
Forces in Action Overview
Newton's First Law 3 of 8 Moment of a force