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Theme A — Space, Time and Motion

A.1.8 Terminal Speed — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 10 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Lesson summary

A.1.8 Terminal Speed — IB PHYSICS SL notes: Explain why a falling object reaches terminal speed and describe how its velocity and acceleration vary with time.In a vacuum — only the weight acts, so the acceleration is g.In a fluid — the weight mg acts downwards and drag acts upwar…

  • At release
  • As speed rises
  • Terminal speed vT
  • Velocity–time
  • Acceleration–time
  • Displacement–time

Part 1 of 7Why a falling body reaches terminal speed

In a vacuum
  • In a vacuum only the weight acts, so the acceleration is g.
In a fluid
  • In a fluid the weight mg acts downwards and drag acts upwards.
At release
  • At release the speed is zero, so drag is zero and a = g.
As speed rises
  • As speed rises drag grows, so the resultant force and the acceleration decrease.
Terminal speed vT
  • Terminal speed vT drag equals weight, the resultant force is zero and the body falls at constant velocity.
  • It occurs for objects falling through a gas or a liquid.

Part 2 of 7Stages of the motion

1
Release — v = 0, drag = 0 and a = g.
2
Speeding up — drag increases, the resultant mg − drag falls and so does a, but the speed still increases.
3
Terminal speed — drag = mg, a = 0 and the velocity is constant.
  • Approach
    • the speed approaches vT without exceeding it, if the body starts slower than vT.

Part 3 of 7Graphs of the motion

Velocity–time
  • Velocity–time the curve starts at the origin with gradient g, flattens progressively and levels off at vT.
Acceleration–time
  • Acceleration–time the curve starts at g and decays to zero.
Displacement–time
  • Displacement–time it starts flat, gets steeper and finally becomes a straight line.
Gradient
  • Gradient on the v–t graph the gradient at any time is the acceleration.
Parachute opening
  • Parachute opening the velocity falls towards a new, smaller terminal speed.

Part 4 of 7What determines terminal speed

Balance condition
  • Balance condition terminal speed is reached when drag at that speed equals the weight.
Quadratic drag
  • Quadratic drag if drag = kv2, then mg = kvT2 and vT = √(mg/k).
Mass
  • Mass a heavier body of the same shape has a higher terminal speed.
Area and shape
  • Area and shape a larger area or drag coefficient lowers the terminal speed.
Skydiver
  • Skydiver about 55 m s−1 spread out, over 80 m s−1 streamlined and about 5 m s−1 with an open parachute.

Part 5 of 7Parachutes and real situations

Opening the parachute
  • Opening the parachute the sudden increase in area makes drag greater than weight, so the resultant force is upwards and the diver decelerates.
Lower terminal speed
  • Lower terminal speed as speed falls, drag decreases until it again equals the weight.
Common idea
  • Common idea the skydiver does not move upwards, but slows to a lower terminal speed.
Raindrops
  • Raindrops they reach terminal speed quickly, otherwise a drop falling from 2 km would reach about 200 m s−1.
Other cases
  • Other cases a ball bearing in oil, a freewheeling cyclist and a vehicle at maximum speed where engine force equals drag.

Part 6 of 7Interpreting data

Terminal speed from data
  • Terminal speed from data plot v against t with a smooth curve and read the value at which the curve becomes horizontal.
Acceleration at a time
  • Acceleration at a time it is the gradient of a tangent drawn at that time.
Drag at a time
  • Drag at a time from mg − F = ma, F = m(g − a).
    What the symbols mean: F = resultant force (N) · m = mass (kg) · a = acceleration (m s−2)
Full explanation
  • Full explanation drag increases with speed, the resultant force decreases, and the acceleration falls to zero when drag equals weight.

Part 7 of 7More from the specification

More from the specification
Velocity-time graph asymptote slope
  • Velocity-time graph asymptote slope downward acceleration decreases continuously as drag grows, until the velocity curve slope reaches zero at terminal speed.
Terminal speed
  • A falling object reaches constant velocity when air resistance equals weight, so net force is zero.
Motion with drag
  • Acceleration decreases as resistance grows with speed, with direction downwards positive.
Projectile motion
  • Horizontal and vertical components are independent;
    • with no resistance vertical motion follows equations of uniform acceleration.
Distance and height
  • Distance and height s = ut + ½at² gives the vertical height, with negative acceleration for upward sign convention.
Resistance on projectiles
  • Drag reduces the range and makes the path asymmetrical.
Velocity-time graph
  • A graph of velocity against time whose gradient is acceleration and area is displacement.
Average speed
  • Total distance divided by total time.
Average velocity
  • Displacement divided by time.
Projectile
  • Object moving under gravity alone in two dimensions.
Distance
  • Total length of path travelled, a scalar.
Resistance
  • Opposition to current, R = V / I, in ohms (Ω).
Vector
  • Quantity with magnitude and direction.
Maximum height
  • The greatest height reached, where the vertical velocity is zero.
Projectile motion
  • Two-dimensional motion with constant horizontal velocity and vertical acceleration g.
Initial velocity
  • Velocity at the start, u.
Kinematic equations
  • Equations relating displacement, velocity, acceleration and time for constant acceleration.

Key terms

TermMeaning
Terminal speedConstant speed reached when drag balances the driving force (weight)
Resultant forceVector sum of all forces on a body
AsymptoteA value a curve approaches but never reaches
WeightGravitational force on a mass, mg
UpthrustUpward buoyant force from a fluid
EquilibriumState with zero resultant force

Avoid these mistakes

1
Saying gravity stops acting — the weight is unchanged and the resultant force falls to zero.
2
Thinking terminal speed means the object stops — it keeps moving at constant velocity.
3
Stating that drag exceeds weight at terminal speed — they are equal.
4
Believing speed decreases as terminal speed is approached — it keeps increasing, only more slowly.
5
Ignoring upthrust in a liquid — it must be included with the drag.

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