Speed and velocity both tell you how fast something is moving — but just like distance and displacement, the difference comes down to direction. Speed is only a number; velocity is that number plus the way you’re heading. Once you’ve got distance vs displacement, this pair follows the exact same pattern.
📘 What you need to know
Speed: how much distance you cover each second. Size only → a scalar.
Velocity: how much your displacement changes each second, with a direction. Size + direction → a vector.
Both are measured in metres per second (m s⁻¹) in SI units.
Velocity can be negative (e.g. moving backwards), but everyday speed is never negative.
Average speed/velocity uses the whole journey; instantaneous speed/velocity is the value at one exact moment.
You can also see other units like km h⁻¹ or mph — convert to m s⁻¹ for physics calculations.
Speed — distance covered per second
Speed simply tells you how quickly the ground goes by. Cover more metres in the same time and your speed is higher. Because there’s no direction attached, speed is a scalar — exactly like distance.
Average speed
average speed = total distancetime taken
For example, if a runner covers 100 metres in 20 seconds, their average speed is 100 ÷ 20 = 5 m s⁻¹. We say average because they probably sped up and slowed down along the way — 5 m s⁻¹ is just the overall rate.
Velocity — displacement per second, with direction
Velocity is the rate at which your displacement changes. Because displacement carries a direction, so does velocity — which makes it a vector. In short, velocity is “speed in a stated direction”.
Average velocityv̄ = change in displacement (s)time taken (Δt)
Same speed, different velocity: both cars do 20 m s⁻¹, but one heads east (+) and one heads west (−). Direction is what separates them.
Quick test: if a ball is thrown straight up at 3 m s⁻¹ and later falls back down past the same point, its velocity flips to −3 m s⁻¹, but its speed is still 3 m s⁻¹ both times. Speed forgets direction; velocity remembers it.
One-line summary: speed = distance ÷ time (scalar). Velocity = displacement ÷ time, with a direction (vector).
Average vs instantaneous
There are two ways to talk about how fast something moves:
Average looks at the whole trip — total displacement divided by total time. Instantaneous is the value at one single instant, like the number your car’s speedometer shows right now.
Finding instantaneous velocity from a graph
On a displacement–time graph, the steepness (gradient) of the line tells you the velocity. If the line is straight, the velocity is constant. If the line curves, the object is speeding up or slowing down, so the velocity is changing. To read the velocity at one exact moment on a curve, you draw a tangent (a straight line that just touches the curve at that point) and find its gradient.
To get the velocity at t = 9 s, draw a tangent and find its gradient: 109 ≈ 1.1 m s⁻¹.
🧭 Recipe — instantaneous velocity from a displacement–time graph
Find the right moment on the time axis (the question always tells you the time).
Draw a tangent that just touches the curve at that point — the gap between curve and line should look even on both sides.
Build a big gradient triangle on the tangent (bigger = more accurate).
Velocity = gradient = rise (change in s)run (change in t)
Worked examples
WE 1
A sprinter’s average speed
A sprinter runs 100 m in a time of 10.49 s. Because she speeds up from a standing start, find her average speed over the race.
Use average speed = distance ÷ timeaverage speed = 100 ÷ 10.49 = 9.5328…average speed = 9.53 m s⁻¹“average” because her actual speed changed throughout the run.
WE 2
Same speed, different velocity
Two cyclists both ride at 8 m s⁻¹ along a straight path, but cyclist A heads east and cyclist B heads west. Taking east as positive, state each one’s velocity.
East is positive, so west is negativeCyclist A: +8 m s⁻¹ (east)Cyclist B: −8 m s⁻¹ (west)same speed (8 m s⁻¹), opposite velocitiesthe minus sign just means “the other way”, not “slower”.
WE 3
Average velocity of a round trip
A jogger runs 400 m around a track in 80 s and finishes exactly where she started. Find her (a) average speed and (b) average velocity.
(a) Average speed uses distance= 400 ÷ 80average speed = 5 m s⁻¹(b) Average velocity uses displacementdisplacement = 0 (back at start)= 0 ÷ 80average velocity = 0 m s⁻¹she clearly moved, but her overall velocity is zero — that’s the displacement talking.
WE 4
Reading velocity off a graph
On a displacement–time graph a tangent is drawn at one instant. Over the tangent, the displacement rises by 10 m while the time runs forward by 9 s. Find the instantaneous velocity at that moment.
Velocity = gradient = rise ÷ run= 10 ÷ 9velocity ≈ 1.1 m s⁻¹a steeper tangent would mean a bigger velocity at that point.
💡 Top tips
Always state a direction with velocity — “5 m s⁻¹ north”, “+12 m s⁻¹”. A velocity with no direction is incomplete.
Convert km h⁻¹ to m s⁻¹ by dividing by 3.6 before using it in a formula.
Average ≠ instantaneous: the average can hide moments where the object was much faster or slower.
Draw a big tangent triangle for graph questions — small triangles make your gradient inaccurate.
⚠ Common mistakes
Using distance for velocity: velocity needs displacement. On a round trip these are very different.
Dropping the direction on velocity — that’s what makes it a vector.
Reading “−” as slower: a negative velocity just means the opposite direction, not a smaller speed.
Confusing average and instantaneous — check which one the question is actually asking for.
Forgetting unit conversion: mixing km h⁻¹ with seconds gives wrong answers.
Up next: Acceleration — how quickly the velocity itself changes. If velocity is “displacement per second”, acceleration is “velocity change per second”.
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