Multi-stage motion

Split the journey at the points where acceleration changes; each stage is its own kinematic problem.

Multi-stage motion0 min · Free lecture

In this lesson

  • Split the journey at the points where acceleration changes; each stage is its own kinematic problem.

Accelerate, cruise, brake: three stages, one journey — the final state of each stage starts the next.

Mark the instants where a changes. For each stage list u, v, a, s, t. The v at the end of stage 1 is the u of stage 2; the positions add.

A v–t sketch of all stages is the fastest sanity check — areas must add up to the total distance.

stotal=s1+s2+s3s_{total} = s_1 + s_2 + s_3

Stages add

Worked example

A body moves with v = 10 m/s for 3 s, then v = 5 m/s for 2 s in the same direction. Find the total distance.

  1. Distance = area under the v–t graph.
  2. 10×3 + 5×2 = 30 + 10 = 40 m.

Answer: 40

Transcript (0 min)
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Multi-stage motion — FemtoLearn.
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Split the journey at the points where acceleration changes; each stage is its own kinematic problem.
Printable notes (free)

Practice

Free · 4 questions with full solutions
  1. Q1 · Numerical · difficulty 2/5

    A body moves with v = 10 m/s for 3 s, then v = 5 m/s for 2 s in the same direction. Find the total distance.

  2. Q2 · Numerical · difficulty 2/5

    The acceleration of a body starting from rest is a = 2 m/s² for 4 s, then zero for 2 s. Find its velocity at t = 6 s.

  3. Q3 · MCQ · difficulty 2/5

    A particle moves with constant velocity. Which a–t graph describes it?

    • A horizontal line at a = 0
    • A horizontal line at a = 2 m/s²
    • A straight line through the origin
    • A parabola
  4. Q4 · MCQ · difficulty 2/5

    The slope of a velocity–time graph gives:

    • Displacement
    • Acceleration
    • Speed
    • Distance