Speed, Velocity and Acceleration
Three quantities that sound similar and are constantly interchanged. The physics is three short formulae; the marks are lost in unit conversion and in which value is initial and which is final.
1. Speed and velocity
Speed = distance ÷ time, in m/s. Speed is a scalar — size only. Velocity = displacement ÷ time, in m/s. Velocity is a vector — size and direction.
Velocity is speed in a stated direction. “5 m/s” is a speed; “5 m/s due north” is a velocity. Questions asking for velocity expect the direction.
A consequence worth knowing: an object moving in a circle at constant speed has a changing velocity, because its direction keeps changing — and a changing velocity means it is accelerating.
Constant speed does not mean zero acceleration if the direction is changing. Confusion between “constant speed” and “constant acceleration” was one of the most-recorded errors in this topic.
Average speed:
average speed = TOTAL distance ÷ TOTAL time
You cannot average the individual speeds, or subtract them. Both errors were recorded. If a journey is 30 m/s for one part and 20 m/s for another, the average is not 25 m/s unless the times are equal. Work out the totals.
Include stationary periods in the total time.
2. Acceleration
Acceleration = change in velocity ÷ time taken a = (v − u) / t
where u = initial velocity, v = final velocity. Units: m/s².
It is FINAL minus INITIAL — v − u, in that order. Reversing it was a recorded error and gives the wrong sign, turning acceleration into deceleration.
“Starts from rest” means u = 0. Misunderstanding this was recorded — a stationary start gives an initial velocity of zero, not the final value.
Example: a car speeds up from 8 m/s to 20 m/s in 4 s.
- a = (20 − 8) ÷ 4 = 3 m/s²
Example: a car slows from 25 m/s to 5 m/s in 4 s.
- a = (5 − 25) ÷ 4 = −5 m/s²
A negative acceleration is DECELERATION — that is the correct result, not an error. You can state it as “a deceleration of 5 m/s²”.
Acceleration is a change of VELOCITY per second, not a velocity. Multiplying velocity by time, or confusing the two, were both recorded. The units tell you: m/s², not m/s.
Rearranging: v = u + at, and t = (v − u)/a.
3. Units — where most marks go
Convert everything to metres and seconds before calculating.
- km → m: × 1000
- minutes → seconds: × 60
- hours → seconds: × 3600
- g → kg: ÷ 1000
- km/h → m/s: ÷ 3.6
Failing to convert minutes to seconds, and grams to kilograms, were both directly recorded. Make the conversion the first line of your working.
Check your final unit is the one asked for. A recorded error gave an answer in “newtons per second” for a speed — the unit is a signal that something has gone wrong upstream.
Match the marks to the detail. Tutors advised looking at the mark allocation: a 1-mark calculation needs the answer; a 3-mark one needs formula, substitution and answer.
4. Free fall and gravity
Near the Earth’s surface, all objects in free fall accelerate downwards at about g = 9.8 m/s² (often taken as 10 m/s²).
Check which value the question or your syllabus uses — 9.8 or 10 — and use it consistently. Using the wrong value was recorded.
Without air resistance, a feather and a hammer fall at the same rate: the acceleration does not depend on mass.
With air resistance, an object reaches terminal velocity when air resistance grows to equal its weight, so the resultant force is zero and it falls at constant velocity.
Terminal velocity means zero acceleration, not zero speed. The object is still moving — steadily.
Resultant force zero means constant velocity (or at rest), never “no motion”. Misunderstanding the resultant force concept was recorded more than once.
5. Distance from a graph
On a speed–time graph, the area under the line gives the distance travelled; the gradient gives the acceleration.
Don’t confuse the area with the gradient. Using the slope to find distance was a specific recorded error — the gradient gives acceleration, the area gives distance.
6. Echo and two-way journeys
For an echo, the sound travels to the surface and back.
Halve the total distance to get the distance to the reflector.
Example: an echo returns after 0.6 s, with sound at 340 m/s.
- Total distance = 340 × 0.6 = 204 m
- Distance to the wall = 102 m
7. Mistakes that cost marks
Confusing speed with velocity, or omitting the direction.
Averaging or subtracting speeds instead of using totals.
Reversing u and v in the acceleration formula.
Treating “from rest” as anything but u = 0.
Multiplying velocity by time to find acceleration.
Treating a negative acceleration as an error.
Not converting minutes, hours, km or grams.
Using the wrong value of g.
Thinking terminal velocity means stopping.
Using the gradient for distance instead of the area.
Forgetting to halve an echo distance.
Giving the wrong unit, or none.
Frequently asked questions
What is the difference between speed and velocity? Speed is a scalar (size only); velocity is a vector — speed in a given direction.
What is the formula for average speed? Total distance ÷ total time.
Can I average two speeds? Only if the times are equal. Otherwise use the totals.
What is the acceleration formula? a = (v − u)/t — final minus initial velocity, over time.
What are the units of acceleration? m/s².
What does a negative acceleration mean? Deceleration — the object is slowing down.
Can something accelerate at constant speed? Yes — if its direction is changing, as in circular motion.
What is g? The acceleration of free fall, about 9.8 m/s² (often taken as 10).
Does a heavier object fall faster? No — not without air resistance. Acceleration doesn’t depend on mass.
What is terminal velocity? The constant velocity reached when air resistance equals weight, so the resultant force is zero.
Quick revision checklist
- I can define speed and velocity and state the difference
- I know velocity needs a direction
- I use total distance ÷ total time for average speed
- I know a = (v − u)/t, final minus initial
- I know “from rest” means u = 0
- I know acceleration is in m/s²
- I know negative acceleration is deceleration
- I know constant speed can still mean accelerating
- I convert km, minutes, hours and grams first
- I know the value of g my syllabus uses
- I know mass doesn’t affect free-fall acceleration
- I can explain terminal velocity via zero resultant force
- I use area for distance on a speed–time graph
- I halve echo distances
- I always write units
These notes cover speed, velocity and acceleration in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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