Motion is the most immediate phenomenon we observe in nature: a ball rolling, a cat crossing the room, a car on the motorway. To describe it fully we need four fundamental quantities.

The quantities of motion

  • tt, time, measured in seconds (s);
  • ss, position, measured in metres (m);
  • vv, velocity, measured in m/s;
  • aa, acceleration, measured in m/s².

A subtle but essential point concerns position: ss is not the “distance travelled”, but the coordinate of the body with respect to a chosen origin. For this reason it can be negative: it depends on where we have fixed the zero and how we have oriented the axis.

A complete description of motion consists in knowing these four quantities instant by instant. The type of motion can be recognised at a glance from the position-time graph: motion at constant velocity (uniform) produces a straight line, while motion at constant acceleration produces a parabola.

Position-time graphs: uniform motion produces a straight line, accelerated motion a parabola.

Try it — interactive simulation

Drag the ball and throw it: the simulation shows the x and y graphs of position, velocity and acceleration, and you can tune the air drag, the surface friction and the bounciness (restitution).

Drag and throw the ball; the graphs show x and y of position, velocity and acceleration, with adjustable air drag, surface friction and restitution.

Topics: Kinematics Concepts: Average velocity · Acceleration

Related exercises: Estimates from the x(t) graph · Ranking the velocity of four cars · Distance from the area under the v-t graph