Also in:Uniform linear motion

Lift Trips: Distance or Displacement?

An educational simulation game. Add up every stretch for the distance, compare start and finish for the displacement, and mind the sign.

DistanceDisplacement

BUILDING / CROSS-SECTION

One way up

Ready
Enable JavaScript to run the lift. The instructions and worked example remain readable.
Distance: every stretchDisplacement ΔyVelocity vStops
Distance and displacements = 0 m · Δy = 0 m

Time

0.0 s

t

Position

0.0 m

y

Velocity

0.0 m/s

v_y

Distance travelled

0.0 m

s = Σ|Δyᵢ|

Displacement

0.0 m

Δy = y − yᵢ

How far will the lift travel?

Read the floors of the trip. Turn floors into heights, add the size of every stretch for the distance, and compare the last floor with the first for the displacement.

Predict the distance and the displacement.

Mission score—

The distance and the displacement each earn 50 points when they are within 0.05 m.

s DistanceΔy Displacement

How to play Lift Trips

  1. Choose a trip and read its floors in order. Each floor is 3 m and up is positive.
  2. Distance: add the size of every stretch the lift travels, ignoring direction.
  3. Displacement: final height minus starting height, with its sign.
  4. Type both and press Play. Compare the trip log and the displacement arrow with your prediction.

Distance adds every stretch; displacement compares start and finish

The distance travelled is a scalar: it adds the size of every piece of the path, so it can only grow and is never negative. The displacement is a vector, here along one vertical axis: Δy = y_final − y_initial. It ignores everything in between, so a round trip has zero displacement, and a trip that ends lower than it started has a negative one. The size of the displacement is never larger than the distance, and they are equal only when the motion never turns back.

A focused learning model

The lift moves at a constant 2 m/s between floors and waits exactly 1 s at each intermediate stop, with no acceleration or braking. Its position is the height of its floor above the ground floor. Floors are exactly 3 m apart. Playback runs 3 times faster than real time.

Changing language keeps your trip, predictions, and progress.