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Velocity–Time Graphs and Terminal VelocityAQA GCSE Physics: Revision notes

Section 1

What Is Acceleration and How Do You Calculate It?

Acceleration is the rate of change of velocity, calculated as:

average acceleration = change in velocity ÷ time taken (a = Δv ÷ t)

  • Acceleration is measured in metres per second squared (m/s²).
  • Deceleration is simply negative acceleration — the object is slowing down.
Key termsaccelerationdeceleration
Example

A car speeds up from 10 m/s to 25 m/s in 5 s. Acceleration = (25 − 10) ÷ 5 = 3 m/s².

Section 2

How Do You Read a Velocity–Time Graph?

On a velocity–time graph:

  • The gradient (slope) of the line represents acceleration.
  • A horizontal line means constant velocity (acceleration = 0).
  • A line sloping upward means the object is accelerating; a line sloping downward means it is decelerating.
  • (HT) The area under the graph (between the line and the time axis) represents the distance travelled during that time interval — for a straight-line section, this can be found using the area of a triangle and/or rectangle.
Key termsvelocity-time graph
Exam tip

Split an irregular area under a velocity–time graph into simple triangles and rectangles, calculate each area separately, then add them together.

Section 3

How Do You Apply the Equation of Motion v² − u² = 2as?

For uniform acceleration, the equation v² − u² = 2as links final velocity (v), initial velocity (u), acceleration (a) and distance travelled (s), without needing to know the time.

Near the Earth's surface, an object in free fall (acted on by gravity alone) accelerates at approximately 9.8 m/s².

Key termsfree fall
Example

An object starts at rest (u = 0) and falls freely for a distance of 20 m. Using v² = 2as = 2 × 9.8 × 20 = 392, so v ≈ 19.8 m/s.

Section 4

What Is Terminal Velocity?

When an object falls through a fluid (such as air or water), two forces act on it: weight (pulling it down) and drag/resistance (opposing motion, increasing with speed).

  1. Initially, weight is greater than drag, so the object accelerates due to gravity.
  2. As speed increases, drag increases too, reducing the resultant force and the acceleration.
  3. Eventually, drag becomes equal in size to weight, so the resultant force is zero and the object stops accelerating.
  4. The object then falls at a constant speed called terminal velocity.

On a velocity–time graph, this shows as a curve that gets less steep over time before levelling off into a horizontal line.

Key termsterminal velocitydrag
Think of it like this

A skydiver initially speeds up quickly, but as air resistance builds up it eventually balances their weight, and they fall at a steady terminal velocity until their parachute opens.

Must Know

  • Acceleration = change in velocity ÷ time (a = Δv/t); deceleration is negative acceleration.
  • On a velocity–time graph, gradient = acceleration; a horizontal line means constant velocity.
  • (HT) The area under a velocity–time graph gives the distance travelled.
  • v² − u² = 2as applies to uniform acceleration; free-fall acceleration near Earth's surface ≈ 9.8 m/s².
  • Terminal velocity occurs when drag force equals weight, giving zero resultant force and constant speed.
  • A falling object's velocity–time graph curves as it accelerates, then flattens out at terminal velocity.

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