Gradient = rate of change
On a distance–time graph the gradient is the speed; on a speed–time graph the gradient is the acceleration. A flat (horizontal) line means "stationary" (distance–time) or "constant speed" (speed–time).
Area under a speed–time graph = distance
Split the area into rectangles and triangles. A rectangle is speed × time; a triangle is base height.
speed = distance ÷ time
Rearrange as needed: , . Keep units consistent.
Drawn from real examiner reports.
Wrong speed–distance–time formula
Writing instead of , or dividing the wrong way round.
Seen on a recent higher-tier exam; the summary asks students to "know how to manipulate the speed, distance, time formula".
Treating times like 9 h 36 min as 9.36
h min is h (since ), not . Convert minutes to a fraction of an hour first.
Seen on a recent higher-tier exam.
Counting squares, not reading the scale
A point was read as because it was "1 square along, 4 squares up" — but each square was not one unit, so the true values were different. Always use the axis scale.
Seen on a recent higher-tier exam.
Average speed as the mean of leg speeds
Average speed for a whole journey is total distance total time, NOT the average of the individual leg speeds. A there-and-back km trip is km total, so use , not .
Confusing area with gradient
On a speed–time graph the GRADIENT is the acceleration and the AREA is the distance. Using speed time for an accelerating (triangular) phase, or the gradient when distance is asked, is a frequent mix-up.
Describe each segment by its gradient
Going up = speeding up / moving away; flat = constant; coming down to 0 on a speed–time graph = decelerating to rest. Read the gradient of each straight section in turn.
State a gradient as a number with units
Acceleration read from a speed–time graph is a single value with units, e.g. — never "2.5x" or an equation of the line. Show rise over run, then state the number.
Convert time and units before dividing
Turn minutes into a fraction of an hour first ( min h, min h), and to change km/h to m/s divide by . Sort units out before you divide, not after.
What does the gradient of a distance–time graph represent?
A train travels km in hour minutes at a steady speed. Find its average speed in km/h.