Problem

Can you match up the following displacement–time graphs with their corresponding velocity–time graphs? Some of the graphs have not been drawn; you will need to complete them yourself.

When you have matched them up, could you give descriptions of what might be happening in them? Here are some possible contexts we’ve thought of; feel free to use your own instead.

  • A baby in a baby-bouncer
  • A toy car being pushed or pulled
  • The ribbon in a tug-of-war game
  • A ball being thrown upwards
  • A yo-yo

(For the distinction between displacement and distance, have a look at Discussing distance. A similar comparison between speed and velocity is found in Speed vs velocity.)

A displacement-time graph with two sharp peaks and troughs.
A displacement-time graph that increases at first, is then flat for a portion, then decreases linearly to 0.
A velocity-time graph that is constantly increasing and becoming more shallow.
A displacement-time graph with two curved peaks and two smooth troughs
A displacement-time graph increasing with fluctuating gradient.
A speed-time graph oscillating around 0.
A displacement-time graph that increases at first, is then flat for a portion, then decreases linearly to 0.
A velocity-time graph, taking a constant positive value.
A linearly increasing displacement-time graph.
A velocity-time graph, starting positive and decreasing more and more quickly going below 0.
A velocity-time graph, going sharply back and forth between two values, spending a portion of time at each of them.
A velocity-time graph, positive for a short period, then 0 for some time, then negative for a short period.
A velocity-time graph, 0 everywhere.
A velocity-time graph, 0 everywhere.
A displacement-time graph, 0 everywhere.
A displacement-time graph, 0 everywhere.