Kinematics graphs at a glance

The x–v–a graph family: slopes and areas chain every pair.

Kinematics graphs at a glance0 min · Free lecture

In this lesson

  • The x–v–a graph family: slopes and areas chain every pair.

Slope down, area up — the two arrows of graph kinematics.

x–t slope → v; v–t slope → a; v–t area → Δx; a–t area → Δv. Every JEE graph question is one of these four arrows.

Signs: areas below the axis are negative; slopes below zero mean decreasing functions.

slopex−t=v,areav−t=Δx\text{slope}_{x-t} = v,\quad \text{area}_{v-t} = \Delta x

The slope-area dictionary

Worked example

The slope of a velocity–time graph gives:

  1. Slope = Δv/Δt = acceleration.

Answer: Acceleration

Transcript (0 min)
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Kinematics graphs at a glance — FemtoLearn.
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The x–v–a graph family: slopes and areas chain every pair.
Printable notes (free)

Practice

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

    The slope of a velocity–time graph gives:

    • Displacement
    • Acceleration
    • Speed
    • 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 · 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.