Area under a Velocity-Time Graph

Meaning of area

Area under a velocity–time graph represents distance travelled

Reason why

Distance = velocity × time, which is the area of the graph

Constant velocity

Area is a rectangle (distance = v × t)

Constant acceleration

Area is a triangle (distance = ½ × base × height)

Changing velocity

Split graph into shapes and add areas

Irregular graph

Divide into rectangles, triangles, trapeziums

Negative area

Represents distance travelled in opposite direction

Total distance

Sum of all positive and negative areas (use magnitudes)

Displacement

Algebraic sum of areas (negatives included)

Units of area

(m/s) × s = m

Graph touching x‑axis

Velocity becomes zero

Graph below x‑axis

Motion reversed

Curved graph

Estimate area using small strips or trapeziums

Key idea

Distance travelled is always the area under the velocity–time graph