Position and displacement

Position is where you are; displacement is how your position changed — a vector, not the distance travelled.

Position and displacement0 min · Free lecture

In this lesson

  • Position is where you are; displacement is how your position changed — a vector, not the distance travelled.

Run a 400 m lap: distance 400 m, displacement zero. Displacement only cares about start and end.

Position x(t) locates the body on the axis. Displacement Δx = x₂ − x₁ is the change in position — a vector with sign. Distance is the total path length, always positive, and generally larger than |displacement|.

On a straight line, sign carries direction: +x and −x. In every kinematics problem, first fix the positive direction and keep it consistent.

Δx=x2−x1\Delta x = x_2 - x_1

Displacement as change in position

Worked example

A particle moves from x = 3 m to x = −5 m. Find the displacement and the distance if it went straight.

  1. Δx = x₂ − x₁ = −5 − 3 = −8 m.
  2. Distance along the straight path = |Δx| = 8 m.

Answer: Δx = −8 m; distance 8 m.

Distance is a scalar; displacement is signed. Most wrong options trade one for the other.
Transcript (0 min)
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Position and displacement — FemtoLearn.
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Position is where you are; displacement is how your position changed — a vector, not the distance travelled.

Frequently asked

Can displacement exceed distance?

Never. Distance ≥ |displacement|.

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

    A body starts from rest with a = 4 m/s². Find the displacement in the 5th second.

  3. Q3 · Numerical · difficulty 2/5

    A body starts from rest and accelerates uniformly at 9.5 m/s². Find the displacement in the 8th second of its motion.

  4. Q4 · 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.