Forces and motion · GCSE Physics
Speed and velocity
Teacher-written GCSE Physics revision on speed and velocity: average speed = distance/time, velocity as a vector, typical speeds, and distance–time graphs where gradient is speed.
Speed is scalar; velocity is speed in a stated direction. Average speed = distance / time. The slope of a distance–time graph is speed.
The important bits
What you need to know
- 1
Distance is how far something has travelled (scalar). Displacement is distance in a given direction from a start point (vector).
- 2
Speed is scalar. Velocity is speed with a direction, so it is a vector. Circular motion at constant speed still has changing velocity because direction changes.
- 3
Average speed = distance / time. Units: m/s. Convert km/h to m/s by dividing by 3.6 (because 1 h = 3600 s and 1 km = 1000 m).
- 4
Typical values worth a sense-check: walking ~1.5 m/s, running ~3 m/s, cycling ~6 m/s, a car in town 13 m/s (about 30 mph), sound in air ~340 m/s.
- 5
Distance–time graphs: straight line up means constant speed; horizontal means stationary; a steeper line means a higher speed; a curve getting steeper means speeding up.
- 6
Gradient of a distance–time graph = speed. Pick two points, rise over run, include units. A closed journey that returns home still has increasing distance if the graph plots distance, not displacement.
- 7
Instantaneous speed is the gradient of a tangent to a curved distance–time graph at that time.
- 8
If you need velocity from a story, state the direction: 12 m/s due north is a velocity; 12 m/s is only a speed.
Quotations worth analysing
Short evidence. Real method.
“Speed is a scalar quantity; velocity is a vector quantity.”
The extra thing velocity has is direction. That is why a car going round a roundabout at 10 m/s has changing velocity.
“The gradient of a distance–time graph is speed.”
Write the scale of each axis before you count squares. Rise is metres; run is seconds; gradient is m/s.
Go deeper
Graphs before algebra
If the paper gives a distance–time graph, they want a gradient, not a memorised story. Pick two points on a straight section, rise over run, include units. A horizontal section is parked, not “constant velocity of zero” as a trick of language — it is zero speed. A curve that gets steeper is speeding up; one that flattens is slowing. Students count squares and then forget the value of each square. Write the scale first: each square is, say, 10 m by 2 s, so a diagonal of 3 up and 4 along is 30 m / 8 s = 3.8 m/s. Distance graphs used at GCSE usually only rise or stay; they do not go negative. If the question plots displacement, a downward slope is motion back towards the origin. Read the axis title.
Go deeper
Unit conversions are part of the physics
A 30 mph limit is about 13 m/s; 70 mph is about 31 m/s. Dividing km/h by 3.6 is the reliable conversion: 72 km/h = 20 m/s. Students multiply by 3.6 when they meant to divide and then cannot see that a “walking speed” of 18 m/s is a sprinting car. Always ask whether the number is plausible. Average speed for a two-part journey is total distance over total time, not the average of the two speeds unless the times happen to match. 30 km at 30 km/h then 30 km at 60 km/h is not 45 km/h: times are 1.0 h and 0.50 h, total 60 km in 1.5 h, so 40 km/h. That non-intuitive result is a classic Higher-style trap built from the definition.
See the idea in action
A cyclist travels 1500 m in 200 s, then rests for 40 s, then travels 900 m in 100 s. Total distance = 2400 m. Total time = 340 s. Average speed = 2400 / 340 = 7.06 m/s. On a distance–time graph that is a straight line of gradient 1500/200 = 7.5 m/s, a horizontal rest, then a line of gradient 9.0 m/s. The average is not 8.25 m/s, because more time was spent on the slower first section. 7.06 m/s is about 25 km/h (multiply by 3.6), a sensible cycling speed.
Exam technique
Turn knowledge into marks
State whether you mean speed or velocity. On a distance–time graph, calculate gradient with units. Convert km/h to m/s by dividing by 3.6. Use typical speeds as a sense-check.
Common mistakes
Do not give these marks away
- 01
Reading a distance–time slope as acceleration, or averaging two speeds without using total distance and total time.
- 02
Leaving speed in kilometres per hour when the rest of the data are in metres and seconds.
- 03
Calling a constant-speed circle a constant-velocity motion.
A car travels 1800 m in 60 s. What is its average speed?
A0.033 m/s
B30 m/s
C108 km/s
D1800 m/s
Show the answer
30 m/s. Average speed = distance/time = 1800 / 60 = 30 m/s (about 67 mph). 0.033 m/s is time/distance. Always metres divided by seconds.
Quick questions
If this is the bit you searched
What is the difference between speed and velocity?
Speed is how fast something moves. Velocity is speed in a stated direction, so it is a vector. Circular motion at constant speed still has changing velocity.
How do you convert 90 km/h to m/s?
Divide by 3.6: 90 / 3.6 = 25 m/s. Or do 90 × 1000 m / 3600 s.
How do you find speed from a distance–time graph?
Calculate the gradient: change in distance divided by change in time on a straight section. Use a tangent for a curved section.
What is a typical walking speed?
About 1.5 m/s. Running is around 3 m/s, cycling around 6 m/s. Use these to check whether an answer is ridiculous.