1 · IGCSE Physics
Distance–time and velocity–time graphs
Drive a car with a speed slider or pick a preset journey and watch both graphs being drawn live. Drag across either graph to read the gradient and the area under the velocity–time graph.
speed v = Δs ÷ Δt (gradient of d–t)
acceleration a = Δv ÷ Δt (gradient of v–t)
distance = area under v–t graph
average speed = total distance ÷ total time
model: s → s + vΔt + ½aΔt², v → v + aΔt (Δt = 0.01 s)
acceleration a = Δv ÷ Δt (gradient of v–t)
distance = area under v–t graph
average speed = total distance ÷ total time
model: s → s + vΔt + ½aΔt², v → v + aΔt (Δt = 0.01 s)
Now: t = 0; s = 0; v = 0; a = 0; average speed = –
At t = 0 s: gradient of d–t = 0; gradient of v–t = 0; area under v–t = 0; distance from d–t = 0
Try this
- Choose “accelerate, cruise, brake”. While the car cruises, read the gradient of the distance–time graph and compare it with the height of the velocity–time graph.
- When the journey ends, set the cursor to 40 s. Check that the shaded area equals the final distance, then confirm it yourself using two triangles and a rectangle.
- In manual mode set the maximum acceleration to 1.0 m s⁻² and change the target speed: see the distance–time graph curve while speed changes and the gold road dots spread apart.
Exam tip: Find acceleration from the gradient of a straight section of a velocity–time graph using a large triangle, and remember the area under that graph gives distance travelled, not speed.