IB Physics HLTopic 1 — Motion, Forces & EnergyPaper 1 & 2Scalars vs vectors~7 min read
Distance vs Displacement
Two words that sound like the same thing but aren’t — and the gap between them is where a lot of easy marks live. Picture running a lap of a track and finishing exactly where you started: you’ve covered plenty of ground, yet you’ve ended up nowhere. That’s the whole idea in a sentence. Distance counts every step; displacement only cares where you finished relative to where you began.
📘 What you need to know
Distance is how far an object travels overall — a scalar, no direction
Displacement is how far it ends up from its start, with direction — a vector
Displacement is the change in position, measured as a straight line from start to finish
Over the same journey, distance is usually larger than the magnitude of displacement
Return to your starting point and the displacement is zero, however far you walked
Combine displacements at right angles with Pythagoras to get the straight-line result
Distance — the scalar
Distance is simply a measure of how far an object travels. It’s a scalar quantity, which means the direction doesn’t matter — you just add up the total ground covered, twists, turns and all. Run a 300 m stretch of a 400 m track and the distance you’ve travelled is 300 m, full stop.
Displacement — the vector
Displacement measures how far something ends up from its starting position, together with the direction. In other words, it’s the change in position — a straight line drawn from where you began to where you finished. Because it carries a direction, it’s a vector, describing both magnitude and direction.
Here’s the mental picture I use with students: think of your walk to school. The distance is every road you actually walked down — every bend, every detour around the park. The displacement is the single straight arrow from your front door to the school gate, cutting through every building and obstacle as if they weren’t there. Same journey, two very different numbers.
Distance vs displacement — the difference
The cleanest way to feel the difference is to walk a path that curves and doubles back, then compare the two.
Distance follows every twist of the route; displacement is the straight arrow from start to finish, direction included.
Consider a 300 m race run on a 400 m oval track. The athletes cover a distance of 300 m — but because the track curves, they finish some straight-line distance from the start, so their displacement is smaller, say 100 m in a particular direction. Run the full 400 m lap back to the start line and the displacement drops to zero, even though the distance is a full 400 m.
distance
→ scalar →
how far travelled
displacement
→ vector →
how far + direction
Quick recap: distance is a scalar (magnitude only); displacement is a vector (magnitude and direction). Same trip, and the distance is never smaller than the displacement’s magnitude.
Adding displacements at right angles
When a journey turns a corner, the total distance is just the sum of the legs — but the displacement is the straight line closing the triangle, found with Pythagoras. Walk 8 m east then 6 m north and you’ve travelled 14 m, yet your displacement is the hypotenuse: 10 m, pointing north-east.
Displacement from perpendicular legs
displacement = √(x2 + y2)
WE 1
A gardener walks around the edge of a rectangular lawn, 12 m by 5 m, following the path A→B→C→D→A back to the start. Find (a) the distance walked and (b) the displacement.
Part (a) — distance is every side added up12 + 5 + 12 + 5 = 34 mdistance = 34 mPart (b) — displacement is start → finish
they end back at A, where they began
displacement = 0 mReturn to the start and displacement is always zero, no matter how far you walked.
WE 2
A hiker walks 8 km due east, then turns and walks 6 km due north. Find (a) the total distance and (b) the magnitude of the displacement.
Part (a) — distance adds the legs8 + 6 = 14 kmdistance = 14 kmPart (b) — displacement uses Pythagoras
the two legs are at right angles
displacement = √(8² + 6²) = √(64 + 36) = √100displacement = 10 km (north-east)Direction matters for a vector — quote it as roughly 37° north of east if asked.
💡 Top tips
Always give displacement a direction — “10 km north-east”, not just “10 km”. A vector without a direction is incomplete.
Watch for return journeys — if the object ends where it started, displacement is zero even though distance isn’t.
Right-angle turns mean Pythagoras — the displacement is the hypotenuse, never the sum of the legs.
Read the question’s wording — “how far travelled” wants distance; “how far from the start” wants displacement.
⚠ Common mistakes
Treating distance and displacement as interchangeable — they’re only equal for straight-line motion in one direction
Quoting a displacement with no direction, so it reads like a scalar
Adding perpendicular legs (8 + 6 = 14) for displacement instead of using Pythagoras
Forgetting that a complete loop gives zero displacement
Up next: Speed vs Velocity — the exact same scalar-versus-vector split, but now applied to how fast you’re going. Distance gives you speed; displacement gives you velocity.
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