What it does
A car moves along a straight road and its graphs draw themselves underneath: position against time (x-t), velocity against time (v-t) and, at the Class 11 level, acceleration against time (a-t). Drag along the graphs (or the time slider) and the car moves to that moment, with its position, velocity and acceleration read out. The area under the v-t graph up to that moment is shaded and shown as the displacement, next to the distance travelled, the average velocity and the average speed.
It follows the school topics on motion in a straight line: distance and displacement, speed and velocity, uniform and non-uniform motion, acceleration and motion graphs (Class 9 Science, describing motion), and instantaneous velocity as a slope and displacement as an area (Class 11 Physics, motion in a straight line). Next, see how the three equations of motion come out of the v-t graph, or measure a real motion from a video with video motion tracker and throw a ball through the air with projectile drag.
How to use it
- Pick a Level. Class 9 shows the x-t and v-t graphs. Class 11 adds the a-t graph, a dashed tangent on the x-t graph (its slope is the velocity at that instant) and the calculus forms v = dx/dt, a = dv/dt and x − x₀ = ∫v dt.
- Stories gives five ready-made motions: a steady walk, speeding up, braking to a stop, stop-and-go, and out-and-back (a ball rolling up a slope and back). Make your own gives you a starting velocity and three 4-second parts with their own acceleration.
- Drive it: press Start and move the slider for 12 seconds. The slider is the velocity you ask for; the car speeds up or slows down at up to 2 m/s² to reach it, so you see a real acceleration on the graphs.
- Match the graph: a dashed target appears on the x-t graph. Press Start and steer so your line lies on it. You get a score out of 100 from the average gap. Show me drives it for you so you can see which velocities make which slopes. New target gives another one.
- Play runs the clock through a story so you can watch the car and the dots on the graphs move together.
Worked example
Choose Stop and go and set the time to 4 s. The car sped up at 1.5 m/s² for 2 s (to 3 m/s), then cruised. The page shows position 9 m, velocity 3 m/s and acceleration 0 m/s². The shaded area under the v-t graph is a triangle (½ × 2 × 3 = 3 m) plus a rectangle (2 × 3 = 6 m), so the displacement is 9 m and the average velocity is 9 ÷ 4 = 2.25 m/s.
Now choose Out and back and move to 10 s. The car went 18 m out, stopped at 6 s and rolled back. The page shows position 10 m, velocity −4 m/s, displacement 10 m but distance travelled 26 m (18 out plus 8 back). The area below the time axis counts as negative.
Tips
- A straight x-t line means steady velocity; a curve means the velocity is changing. Steeper means faster.
- On a v-t graph, the slope is the acceleration and the area is the displacement.
- When the v-t line crosses zero, the car turns round: the x-t graph has a peak or a valley there.
FAQ
Why are distance and displacement different? Displacement is how far you end up from the start, with a direction; distance is the whole length of the path. They are the same only if the car never turns back.
What does a negative velocity mean? The car is moving backwards (to the left on the road). Speed is the size of the velocity, so it is never negative.
Is anything saved? No. The questions in Check yourself are made fresh each time and checked in your browser; nothing is stored or sent.
Where the numbers come from
- Kinematics of straight-line motion with constant acceleration in each part (x = x₀ + ut + ½at², v = u + at) and the meaning of slope and area on motion graphs: standard school physics found in any textbook.
- Displacement and distance checked against an independent NumPy trapezium integration of v(t) on 2,000,001 points. The ready-made motions and questions use made-up, round numbers.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
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Last updated 2026-11-09.