In reality the motion of a body is often composed of several phases: acceleration, constant velocity, braking. The idea is to apply the equations of motion segment by segment, and the event table becomes the fundamental working tool.

Strategy for motion in multiple segments

  1. Identify the events (changes of regime: start, end of acceleration, start of braking, stop) and number the segments between them.
  2. Build the event table with the four quantities; the acceleration of each segment goes in the intermediate row.
  3. In each segment the acceleration is constant: apply the four equations, choosing each time the one with a single unknown.
  4. The final value of one segment (position, velocity, time) is the initial value of the next segment: the segments “glue together” event after event.

The strength of the method lies precisely in this gluing together: a complicated motion becomes a chain of simple uniformly accelerated motions, each solvable with the basic equations. Two worked examples show the method in action: Carlo’s journey (three segments: acceleration, constant velocity, braking) and The two-phase cat (where the table reveals a counterintuitive fact about the sign of the velocity).

Try it — interactive simulation

The ball slides under gravity along the curve: where the slope is steeper it accelerates more. Watch the speed change from segment to segment.

Topics: Kinematics Concepts: Uniformly accelerated motion Skills: Choice of axes Methods: Resolution into Cartesian components

Related exercises: Carlo’s journey · Stopping distance (reaction and braking) · Proof of the time-free equation