Speed–Time Graphs

A speed–time graph shows how an object’s speed changes with time. Time is on the horizontal (x) axis in seconds (s). Speed is on the vertical (y) axis in metres per second (m/s). It is different from a distance–time graph. Here, the slope tells you acceleration, not speed.

Reading the shape

• At rest: a horizontal line on the time axis (speed = 0).
• Constant speed: a horizontal line above the axis (flat line, speed not changing).
• Accelerating: a line sloping up; steeper means speed increases faster.
• Decelerating: a line sloping down; acceleration is negative.
• Curved line: changing acceleration (not constant).

Key formulas

Average speed: $v = \dfrac{s}{t}$. Acceleration: $a = \dfrac{\Delta v}{\Delta t}$.

On a speed–time graph: gradient (slope) = acceleration; area under the graph = distance travelled.

$$\text{distance} = \text{area under speed–time graph}$$

Finding acceleration (from gradient)

For a straight line, pick two points: $a = \dfrac{\text{change in speed}}{\text{change in time}} = \dfrac{\Delta v}{\Delta t}$. A positive gradient means speeding up; a negative gradient means slowing down.

Finding distance (from area)

• Rectangle (constant speed): area = base × height = time × speed.
• Triangle (speed changing uniformly): area = $\tfrac{1}{2} \times$ base × height.
• Trapezium (two different speeds): area = average of parallel sides × base.

Unit check: (m/s) × s = m.

Common misconceptions

• Thinking the height of the line shows distance. It shows speed; distance is the area under the line.
• Confusing speed–time with distance–time: on distance–time graphs, slope = speed; here, slope = acceleration.
• Using wrong units for acceleration (should be m/s²).
• Expecting negative speeds: speed is never negative (velocity can be).

Drawing and reading tips

• Label axes with units: time (s), speed (m/s). Use even scales.
• Plot neat crosses and draw a thin best-fit line when appropriate.
• When lines are straight, use the gradient for acceleration and simple areas for distance.