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Vectors, Scalars & Motion in One Dimension: Misconceptions

≈ 30 min
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Misconceptions

Test common incorrect explanations against definitions, conservation rules and evidence.

This extension applies that lens specifically to Vectors, Scalars & Motion in One Dimension.

Two kinds of quantity

Every measurement in physics is either a scalar or a vector.

  • A scalar has only size (magnitude): time, distance, speed, mass, energy.
  • A vector has size and direction: displacement, velocity, acceleration, force.

When you say a taxi drove 11 km, that is a distance (scalar). When you say it ended up 5 km north of the rank, that is a displacement (vector) - direction matters.

Describing motion in a straight line

We pick one direction as positive (say, right or north is ++). Then motion to the other side is negative.

Displacement Δx\Delta x is the straight-line change in position from start to finish, with direction. Distance is the total path length travelled.

Average velocity is displacement per unit time:

vav=ΔxΔtv_{av} = \frac{\Delta x}{\Delta t}

Average speed is distance per unit time. If an object goes out and comes back, its displacement (and average velocity) can be small or zero while its distance (and average speed) is large.

Acceleration is the rate of change of velocity:

a=ΔvΔt=vf−viΔta = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{\Delta t}

measured in metres per second per second, m⋅s−2\text{m}\cdot\text{s}^{-2}.

Physics: Motion, Waves & Electricity — Misconceptions: Which one of the following is a vector quantity?

Physics: Motion, Waves & Electricity — Misconceptions: A minibus travels 800 m800\,\text{m} north, then 300 m300\,\text{m} south, taking 100 s100\,\text{s} altogether. Taking north as positive, calculate the magnitude of its average velocity in m/s\text{m/s}.

Physics: Motion, Waves & Electricity — Misconceptions: On a straight road a car's velocity increases uniformly from 6 m/s6\,\text{m/s} to 18 m/s18\,\text{m/s} in 4 s4\,\text{s}. Calculate its acceleration in m⋅s−2\text{m}\cdot\text{s}^{-2}.

Name the original topic being extended by this misconceptions lesson.

Which statement is the best evidence-led starting point for Vectors, Scalars & Motion in One Dimension: Misconceptions?