Acceleration–time graphs

a–t graph: area = change in velocity; slope of v–t is a — work upward from a to x.

Acceleration–time graphs0 min · Free lecture

In this lesson

  • a–t graph: area = change in velocity; slope of v–t is a — work upward from a to x.

The a–t graph feeds the v–t graph, which feeds the x–t graph. Chain the areas.

Area under a–t = Δv. Given a(t), integrate once for v(t) and again for x(t) — or chain the graph areas.

Constant a shows as a horizontal line on a–t; zero area means no net velocity change.

Δv=∫a dt\Delta v = \int a\, dt

Velocity change as the a–t area

Worked example

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.

  1. Area under the a–t graph = change in velocity.
  2. Area = 2 m/s² × 4 s = 8 m/s (the last 2 s add nothing).

Answer: 8

Transcript (0 min)
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Acceleration–time graphs — FemtoLearn.
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a–t graph: area = change in velocity; slope of v–t is a — work upward from a to x.
Printable notes (free)

Practice

Free · 4 questions with full solutions
  1. Q1 · 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.

  2. Q2 · 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
  3. Q3 · 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.

  4. Q4 · MCQ · difficulty 2/5

    The slope of a velocity–time graph gives:

    • Displacement
    • Acceleration
    • Speed
    • Distance