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Theme A — Space, Time and Motion

A.1.1 Distance and Displacement — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 3 of 63 1 quiz

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Lesson summary

A.1.1 Distance and Displacement — IB PHYSICS SL notes: Distinguish scalar distance from vector displacement and calculate each for straight and bent paths.Scalar — a quantity with magnitude only, e.g.

  • Reference point
  • Projectile
  • Resistance
  • Scalar — a quantity with magnitude only, e.g. mass, time, energy and distance
  • Vector — a quantity with magnitude and direction, e.g. displacement, velocity, acceleration and force
  • Scalars add as ordinary numbers; vectors must be added taking direction into account

Part 1 of 7Scalars and vectors

Scalar
  • Scalar a quantity with magnitude only, e.g. mass, time, energy and distance.
Vector
  • Vector a quantity with magnitude and direction, e.g. displacement, velocity, acceleration and force.
Scalars add as ordinary numbers; vectors must be added taking direction into account.
In one dimension choose a positive direction and give vectors a sign, e.g. −4 m is 4 m in the negative direction.

Part 2 of 7Distance

Distance
  • Distance a measure of how far an object travels; the total length of the path.
It is a scalar in metres and direction is not important; it cannot be negative or decrease.
A car odometer records distance.
The athletes in a 300 m race on a 400 m track travel a distance of 300 m.

Part 3 of 7Displacement

Displacement
  • Displacement how far something is from its starting position, with direction; the change in position.
It is a vector measured in metres; only the end points matter, not the route.
For one dimension, displacement = final position − initial position (Δx = xf − xi).
  • It can be positive, negative or zero.
Its size is never greater than the distance travelled.
  • They are equal only for straight-line motion without reversing.

Part 4 of 7Distance compared with displacement

FeatureDistanceDisplacement
TypeScalarVector
DirectionNot neededNeeded
ValueNever negativePositive, negative or zero
Depends onWhole routeStart and end points only
One full lap of a trackLength of the lapZero
Student going to schoolTotal length of roads with twistsStraight line from home to school

Part 5 of 7Adding displacements in two dimensions

1
Draw the displacement vectors head to tail.
2
The resultant runs from the tail of the first to the head of the last.
3
For two perpendicular legs a and b the magnitude is s = √(a2 + b2).
4
The direction from the first leg is θ = tan−1(b ÷ a).
5
For non-perpendicular legs resolve each vector into components, add the components, then recombine.
6
A scale diagram with ruler and protractor is also acceptable.

Part 6 of 7Reading questions and choosing a coordinate system

1
"Total path length" means distance; "how far from the start" means the magnitude of displacement.
2
State a reference point (origin) and positive direction before using signs.
3
Position is measured from the origin; displacement is a difference between two positions and does not depend on the origin.
4
Give vector answers with a direction or sign, and keep SI units (metres).

Part 7 of 7More from the specification

More from the specification
Distance and displacement
  • Distance and displacement distance is a scalar path length while displacement is a vector from start to end
Projectile motion
  • Projectile motion the horizontal velocity stays constant and the vertical motion has constant acceleration due to gravity,
  • so components are treated independently
Air resistance
  • Air resistance drag increases with speed and makes real trajectories lower in height and range, leading to terminal speed
Graphs
  • Graphs displacement-time gradient gives velocity, and equations of motion apply for constant acceleration
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.
Fluid resistance
  • Drag force from a fluid opposing motion.
Average speed
  • Total distance divided by total time.
Average velocity
  • Displacement divided by time.
Projectile
  • Object moving under gravity alone in two dimensions.
Resistance
  • Opposition to current, R = V / I, in ohms (Ω).
Constant
  • Not changing.
Terminal
  • Connection point of a cell, labelled + or −.
Gradient
  • Slope of a graph line.
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.

Key terms

TermMeaning
ScalarA quantity with magnitude only.
VectorA quantity with magnitude and direction.
DistanceTotal length of path travelled; scalar.
DisplacementStraight-line change in position with direction; vector.
ResultantSingle vector equivalent to several added vectors.
Reference pointOrigin from which positions are measured.

Avoid these mistakes

1
Using distance when displacement is asked, and the reverse.
2
Saying displacement cannot be zero — a return trip has non-zero distance and zero displacement.
3
Adding perpendicular displacements arithmetically — use Pythagoras or components.
4
Quoting a displacement without a direction or sign.

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