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
- Identify the events (changes of regime: start, end of acceleration, start of braking, stop) and number the segments between them.
- Build the event table with the four quantities; the acceleration of each segment goes in the intermediate row.
- In each segment the acceleration is constant: apply the four equations, choosing each time the one with a single unknown.
- 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
Links
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