What we're doing: You walk 5 m from the sofa to the fridge, then 2 m back towards the sofa.
Your legs walked 7 m, but you are only 3 m from where you started.
Here you will learn a name for each answer.
How far you went (distance)
- Add up every metre of the path: 5 + 2 = 7 m
- Only a size, no direction
- It never goes down while you keep moving
Where you ended up (displacement)
- The straight line from start to finish: 3 m towards the fridge
- A size and a direction
- It is zero if you come back to the start
Spot it: Displacement is your change in position: where you are now compared with where you started.
Distance is a size only (a scalar). Displacement is a size and a direction (a vector).
On a straight line, show the direction with a sign. Call towards the fridge + and back towards the sofa −.
Then the displacement is +5 − 2 = +3 m: 3 m on the fridge side of the sofa.
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A delivery robot drives 3.0 m east, turns, and drives 4.0 m north.
The two moves meet at a right angle, so the straight line from start to finish is the long side of a right-angled triangle.
Solid arrows: the path the robot drove. Dashed arrow: straight from start to finish.
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- size of the displacement (m)
- the east–west move (m)
- the north–south move (m)
A delivery robot drives 3.0 m east and then 4.0 m north. Determine the displacement of the robot.
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Same split, one step on: A dog runs 40 m to fetch a ball and 40 m straight back to its owner, in 20 s.
It was clearly moving quickly, yet it ended up exactly where it began. Speed and velocity give two different answers.
Speed is how fast the distance piles up. Velocity is how fast your position changes, and in which direction (the rate of change of position).
- the whole length of the path (m)
- the time taken (s)
- change in position = displacement (m)
- time taken (s)
A memory aid: cover the quantity you want. s = v × t, v = s ÷ t, t = s ÷ v.
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A dog runs 40 m in a straight line to fetch a ball, then 40 m straight back to its owner. The whole trip takes 20 s.
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Over a trip, or at one moment?: A car pulls away from traffic lights and covers 10 m in the first 4 s. On average that is 2.5 m every second.
The value at one moment: But the car is speeding up, so at 4 s its speedometer reads more than 2.5. The value at one moment is the instantaneous value.
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How to find each one: Average: the whole change in position ÷ the whole time.
Instantaneous: the slope of the tangent to the position–time graph at that moment. Or time a very short stretch, so short that the speed hardly changes during it.
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How this is tested: Usually a multiple-choice question: pick the right definition, or work out an average speed and an average velocity for a trip in two parts.
The trap: Giving the distance when the question asks for the displacement. Read which one the question names before you add anything.
The cyclist's ride: path (solid) and displacement (dashed).
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A student cycles 1.2 km due north and then 0.50 km due east. The ride takes 5.0 minutes.
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