From graphs to motion: reading the story

Translate a graph into a story: where is the body, how fast, accelerating or braking, turning around?

From graphs to motion: reading the story0 min · Free lecture

In this lesson

  • Translate a graph into a story: where is the body, how fast, accelerating or braking, turning around?

A graph is a biography of the motion — read it chronologically.

Ask four questions of every graph: (1) initial value? (2) slope sign? (3) slope magnitude changing? (4) crossings of the axis? The answers give rest, motion, acceleration, and reversal.

The body turns around where velocity crosses zero with a sign change — the most common hidden event in graph questions.

v=dxdt, a=dvdtv = \frac{dx}{dt},\ a = \frac{dv}{dt}

Graph slopes as derivatives

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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From graphs to motion: reading the story — FemtoLearn.
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Translate a graph into a story: where is the body, how fast, accelerating or braking, turning around?
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