Speed — distance travelled per unit time
Speed is the distance travelled per unit time: , measured in metres per second (m/s), with in metres and in seconds. Average speed = total distance ÷ total time. It is one value for a whole journey, so it still works when the object speeds up and slows down — but it says nothing about the speed at any single instant. Convert to SI units before substituting: .
Motion graphs — gradient and area
On a distance-time graph the gradient is the speed: a flat line means stationary, a straight slope constant speed, a steeper slope a greater speed, a curve a changing speed. On a speed-time graph the area under the line is the distance travelled: a flat line means constant speed, a line sloping up accelerating and one sloping down decelerating, and its gradient gives the acceleration (Extended). Read the axis labels first.
(Extended) Velocity, acceleration and free fall
Velocity is speed in a given direction — a vector with magnitude and direction (m/s). Acceleration is the change in velocity per unit time, , in . A straight sloping speed-time line = constant (uniform) acceleration, a curve = changing. A deceleration is a negative acceleration. In free fall near Earth, is roughly constant at about : a body dropped from rest gains about each second.
Drawn from real examiner reports.
Distance = area, not max speed × time
To get the distance from a speed-time graph, find the area under the line. Maximum speed × total time over-counts, because the object was not at maximum speed for the whole journey; and the gradient gives the acceleration, not the distance. Split the area into rectangles and triangles and add them — equivalently, average speed × time.
Flagged Jun 2022 P11 Q28; Jun 2023 P32 Q12biii; Nov 2023 P11 Q28 — the most repeated physics calculation error
Missing units and missed conversions
A numerical answer without its unit is not fully credited — m/s for speed, for acceleration, m for distance. Convert to SI before substituting rather than after: km to m, h to s, cm to m. Quoting a "formula" built out of units, or mixing words, symbols and units in one expression, also loses credit.
Average speed is not speed at an instant
Average speed = total distance ÷ total time for the whole journey. It is not the speed at any one moment and it is not the maximum speed. A sprinter covering 100 m in 12.5 s has an average speed of 8.0 m/s even though her top speed is higher. When a question says "average", use the totals — do not hunt for an instantaneous value.
(Extended) Deceleration keeps its minus sign
Braking is a negative acceleration, and handles it unchanged. A train slowing from 30 m/s to rest in 10 s gives . Only the sign of differs from a speed-up; there is no separate "deceleration formula". Dropping the minus sign loses the mark.
Flat line: stationary or constant speed?
A horizontal line means stationary on a distance-time graph (distance not changing) but constant speed on a speed-time graph — the object is still moving. Never read a distance-time graph as a speed-time graph: its gradient is the speed, and the area under it is meaningless. On a speed-time graph the steepest gradient shows the greatest acceleration (Extended).
Flagged Jun 2023 P32 Q12bii
(Extended) Velocity is a vector, speed is not
Speed is a scalar (magnitude only); velocity is speed in a given direction — magnitude AND direction. An object at constant speed but changing direction (a roundabout car, a rotating blade tip) has a changing velocity. "The velocity is constant because the speed does not change" is wrong. Acceleration is change of velocity, so changing direction is accelerating.
Flagged Nov 2023 P41 Q3ciii — velocity of a rotating blade changes because its direction changes
Formulas rearranged upside down
Speed is , not ; acceleration is , not . Write the formula, substitute, then rearrange — never guess which quantity belongs on top. An inverted answer reads as perfectly plausible, so sanity-check the size: 150 m covered in 20 s must come out as a few m/s, not a fraction of one.
Identify the graph before calculating
Read the -axis label first. Distance on means a distance-time graph: gradient = speed. Speed on means a speed-time graph: gradient = acceleration, area = distance. Only then decide whether the question wants a gradient or an area — they answer different questions.
Take a gradient from two far-apart points
A gradient is a change divided by a change: pick two clearly separated points on the line and divide the change on the -axis by the change on the -axis. Points close together magnify the reading error. Never read a single coordinate off the graph and use it on its own.
Match the points to the mark tariff
A 3-mark "describe the motion" needs three separate features — one per section of the graph — not one long sentence about the first section. True but off-question detail earns nothing. Where sections are compared, say which is faster and why (steeper = greater speed).
Match the command word
State — one line of fact. Describe — say what the motion is ("constant speed, then decelerating"). Explain — say why, from the graph shape; describing when an explanation was asked scores nothing. Calculate — show formula, substitution, answer with unit.
Cambridge 0654 spec reference: Section P1 "Motion, forces and energy", sub-topic P1.2 (Core + Extended). This leaf covers the Core ideas of speed and average speed, distance-time and speed-time graphs, and reading the state of motion from a graph, plus the Extended ideas of velocity, acceleration (), constant vs changing acceleration, deceleration as a negative acceleration, and the acceleration of free fall.
Scope note: this topic uses only graph (gradient/area) methods and -- there are NO equations-of-motion (SUVAT) calculations in 0654, and momentum is not part of the current syllabus.
(Core) Speed: where = speed (m/s), = distance travelled (m), = time taken (s).
(Core) Average speed:
(Core) Speed from a distance-time graph = gradient:
(Core) Distance from a speed-time graph = area under the line.
(Extended) Acceleration: where = acceleration (), = change in velocity (m/s), = time taken (s). A deceleration gives a negative value of .
(Extended) Acceleration of free fall near the Earth: (approximately constant).
(Core) Define speed and give the formula and unit.
A model car travels a distance of along a straight track in a time of at a steady speed.
Calculate the speed of the car. (2 marks)
