Dimensional sanity checks in kinematics

Every answer must have the right dimensions: m, m/s, m/s² — a one-second sanity filter.

Dimensional sanity checks in kinematics0 min · Free lecture

In this lesson

  • Every answer must have the right dimensions: m, m/s, m/s² — a one-second sanity filter.

An answer in metres for a velocity question is wrong before you even read the options.

Check the dimensions of every computed quantity: displacement [L], velocity [LT⁻¹], acceleration [LT⁻²], time [T].

If a formula mixes lengths and velocities without the right powers, something is wrong — the dimensional filter catches most algebra slips instantly.

[x]=L, [v]=LT−1, [a]=LT−2[x] = L,\ [v] = LT^{-1},\ [a] = LT^{-2}

Dimensions of kinematic quantities

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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Dimensional sanity checks in kinematics — FemtoLearn.
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Every answer must have the right dimensions: m, m/s, m/s² — a one-second sanity filter.
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