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Theme A — Space, Time and Motion

A.1.3 Acceleration — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 5 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

A.1.3 Acceleration — IB PHYSICS SL notes: Define acceleration, calculate it from changes in velocity and interpret its sign and direction for speeding up and slowing down.Acceleration = the rate of change of velocity; it is a vector with unit m s−2.An acceleration of 3 m s−2 mean…

  • Average acceleration
  • What the symbols mean
  • Change of direction
  • Deceleration
  • Zero velocity
  • Uniform acceleration

Part 1 of 7Definition of acceleration

Acceleration
Acceleration the rate of change of velocity; it is a vector with unit m s−2.
  • An acceleration of 3 m s−2 means the velocity changes by 3 m s−1 every second.
Average acceleration
  • Average acceleration a = Δv / Δt = (v − u) / t.
    What the symbols mean: a = acceleration (m s−2) · v = final velocity · u = initial velocity (m s−1) · Δv = change in velocity · t = time taken (s)
  • u is the initial velocity, v the final velocity and t the time taken.
  • The change in velocity Δv is final velocity minus initial velocity.
Direction
  • Direction acceleration points in the direction of the change in velocity.
Change of direction
  • Change of direction velocity is a vector, so turning at constant speed is also an acceleration.
  • Circular motion is the main case.

Part 2 of 7Sign and direction

VelocityAccelerationMotion
PositivePositiveSpeeding up forwards
PositiveNegativeSlowing down
NegativeNegativeSpeeding up backwards
NegativePositiveSlowing down while moving backwards
Deceleration
  • Deceleration an informal word for acceleration opposite to the velocity;
    • physically it is still an acceleration.
Zero velocity
  • Zero velocity it does not mean zero acceleration.
  • A ball at the top of its flight has v = 0 but a = −9.8 m s−2.

Part 3 of 7Uniform and non-uniform acceleration

Uniform acceleration
  • Uniform acceleration constant in size and direction.
  • Free fall near Earth's surface without air resistance has g = 9.8 m s−2.
  • A constant resultant force on a fixed mass gives uniform acceleration.
Non-uniform acceleration
  • Non-uniform acceleration the value changes with time.
  • The formula a = Δv / Δt then gives only the average acceleration.
  • The instantaneous acceleration is the gradient of the tangent on a velocity–time graph.

Part 4 of 7Acceleration and graphs

Velocity–time gradient
  • Velocity–time gradient it is the acceleration.
  • A straight sloping line is constant acceleration and a horizontal line is zero acceleration.
  • A curve means the acceleration is changing.
Crossing the time axis
  • Crossing the time axis the object stops instantaneously and reverses direction.
Acceleration–time area
  • Acceleration–time area it equals the change in velocity.
Area under the v–t graph
  • Area under the v–t graph it gives the displacement.

Part 5 of 7Finding acceleration

Finding acceleration
From velocities and time
  • From velocities and time a = Δv / Δt.
From a velocity–time graph
  • From a velocity–time graph take the gradient, using a large triangle or a tangent.
From Newton's second law
  • From Newton's second law a = F / m, using the resultant force.
From uniform acceleration from rest
  • From uniform acceleration from rest a = 2s / t2.
In g units
  • In g units the g-force is the acceleration divided by 9.8 m s−2.

Part 6 of 7Measuring acceleration

Two light gates
  • Two light gates a trolley with a card gives speeds u and v and a timer gives the interval t, so a = (v − u) / t.
Motion sensor
  • Motion sensor it plots velocity against time and the gradient gives the acceleration directly.
Reducing uncertainty
  • Reducing uncertainty repeat the measurement and use a long enough run.
Typical values
  • Typical values family car 2 to 3 m s−2, braking 7 to 8 m s−2, free fall 9.8 m s−2.

Part 7 of 7More from the specification

More from the specification
Acceleration slope across experimental velocity range
  • Acceleration slope across experimental velocity range the linear gradient slope of a velocity-time graph determines acceleration over a specified speed range.
Kinematic Equations for Constant Acceleration
  • The motion of an object under uniform acceleration is resolved using kinematic equations relating five key kinematic quantities: displacement s, initial velocity u, final velocity v, acceleration a,
    • (such as an accelerating cyclist)
  • and time t.
Independent Components of Projectile Motion
  • In ideal projectile motion, horizontal motion has constant velocity with zero acceleration,
  • while vertical motion undergoes constant gravitational acceleration acting downward.
    • (g = 9.81 m s-2
Maximum Height of a Projectile
  • The maximum vertical height reached by a launched projectile occurs when vertical velocity becomes momentarily zero (vy = 0), calculated using the kinematic equation hmax = (u * sin(theta))2 / (2 * g).
Terminal Velocity in Fluid Resistance
  • An object falling through a fluid accelerates until downward weight equals upward drag force,
  • resulting in zero net force and a constant terminal velocity over subsequent distance fallen.
Fluid resistance
  • Drag force from a fluid opposing motion.
Scalar quantity
  • A quantity with magnitude only, such as potential
Vector quantity
  • A quantity with both magnitude and direction.
Projectile
  • Object moving under gravity alone in two dimensions.
Distance
  • Total length of path travelled, a scalar.
Terminal
  • Connection point of a cell, labelled + or −.
Terminal velocity
  • Constant speed when air resistance equals weight.
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.
Kinematic equations
  • Equations relating displacement, velocity, acceleration and time for constant acceleration.
Velocity-time graph
  • A graph of velocity against time whose gradient is acceleration and area is displacement.

Key terms

TermMeaning
AccelerationRate of change of velocity; a vector in m s−2
Uniform accelerationAcceleration that stays constant in size and direction
DecelerationInformal term for acceleration opposite to the velocity
Free fallMotion under gravity alone, with acceleration g
Initial velocity (u)Velocity at the start of the time interval
Instantaneous accelerationAcceleration at one moment; gradient of the tangent on a v–t graph

Avoid these mistakes

1
Treating acceleration as how fast the object moves — it is how quickly the velocity changes.
2
Thinking zero velocity means zero acceleration — acceleration can be non-zero at an instant of rest.
3
Treating deceleration as a separate quantity — it is a negative acceleration in the positive direction.
4
Using speeds instead of velocities when direction reverses — use signed velocities.
5
Writing the unit as m s−1 — acceleration is in m s−2.

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