The big idea: Speed = how fast you go. Velocity = how fast and in which direction.
Distance = the whole path you travel. Displacement = the straight line from start to finish (with direction).
Scalars (size only)
- speed — e.g. 30 m s⁻¹
- distance — e.g. 7 m
Vectors (size + direction)
- velocity — e.g. 30 m s⁻¹ east
- displacement — e.g. 5 m north-east
Quick example: Walk 3 m east, then 4 m north. You walk 7 m of path — but you end up only 5 m in a straight line from where you started:
[Diagram: phys-distance-displacement] - Available in full study mode
The two parts of the walk meet at a right angle, so the straight-line displacement is the hypotenuse of the triangle — find it with Pythagoras:
Velocity (or speed) is how much displacement (or distance) you cover each second:
- velocity / speed (m s⁻¹)
- displacement / distance (m)
- time taken (s)
Not in the data booklet — so remember it: Unlike the suvat equations, v = displacement ÷ time is not given — you have to know it. Use the formula triangle: cover the quantity you want and read off the rest.
[Diagram: phys-formula-triangle] - Available in full study mode
Worked example — average speed
A runner covers 100 m in 12.5 s. What is their average speed?
Solution
- Speed = distance ÷ time:
- Now put in the numbers:
- Work it out — keep the unit:
Final answer
average speed = 8.0 m s⁻¹.
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Average vs instantaneous velocity: Average = over a whole trip (displacement ÷ time).
Instantaneous = at one moment — what a speedometer shows right now.
On a drive your average might be 50 km h⁻¹, but your instantaneous speed is 0 at a red light and 90 on the motorway.
IB-style question — (a) average speed
A cyclist covers 180 m in 60 s. Find her average speed for the ride.
Solution
- Average speed = distance ÷ time:
- Put in the numbers:
- Work it out — keep the unit:
Final answer
average speed = 3.0 m s⁻¹.
IB-style question — (b) average or instantaneous?
During that same ride, her bike computer reads 7 m s⁻¹ at one moment. Is that an average or an instantaneous speed?
Solution
- The average is worked out over the whole ride — that's the 3.0 m s⁻¹ from part (a).
- A live reading at one moment is the instantaneous speed.
Final answer
7 m s⁻¹ is the instantaneous speed (at that moment); 3.0 m s⁻¹ is the average over the whole ride.
IB-style question — which one is instantaneous velocity?
Which statement best defines an object's instantaneous velocity?
(A) the total distance travelled ÷ the total time
(B) the rate at which its position changes at a single instant
(C) the total displacement ÷ the total time
(D) the rate at which the distance travelled increases
Two quick checks
- Uses distance? Then it's speed, not velocity → cross out (A) and (D).
- Says '÷ total time'? That's the average → cross out (C).
- Left with (B) — the velocity at a single instant. ✓
Final answer
B — the value right now. (A = average speed · C = average velocity · D = speed.)
How this is tested: Speed, velocity, distance and displacement are the foundation of kinematics.
- Paper 1A: quick concept MCQs — e.g. the definition of instantaneous velocity, or distance vs displacement. - Paper 1B / Paper 2: you use them in every motion calculation.
Classic trap: anything that returns to its start has zero displacement (and zero average velocity), even though it still covered a distance.
IB-style question — (a) average speed
A runner completes one full lap of a 400 m track in 80 s, finishing exactly where they started. Find the average speed.
Solution
- Average speed uses the distance — the whole path travelled:
- Put in the numbers:
- Work it out, keep the unit:
Final answer
average speed = 5.0 m s⁻¹.
IB-style question — (b) average velocity
The same runner: one 400 m lap in 80 s, finishing where they started. Find the average velocity.
Solution
- Average velocity uses the displacement (start → finish), not the path:
- Finishing where you started means the displacement is zero:
- So the average velocity is:
Final answer
average velocity = 0 — the displacement is zero (back to the start), even though the distance was 400 m.