Describe the motion from the shape of the line

What does the slope of a position-time graph at a moment give?

A model train makes a 9 s run along a straight 10 m track, in four stages. Stage 1: from the 1 m mark it rolls forward steadily, gaining 2 m each second for 2 s. Stage 2: it sits still at the 5 m mark for 2 s. Stage 3: it moves off again, covering more track each second, and passes the 9 m mark at 6 s. Stage 4: it slows, covering less track each second, and creeps up to the 10 m mark.

Segment A is stage 1: the train gains the same 2 m every second. A straight sloped line, an unchanging slope: constant velocity.

Segment B is stage 2: the train sits at the 5 m mark while time passes. A flat line, slope zero: at rest.

In this topic, 'constant velocity' names steady motion at a velocity that is not zero. When the constant velocity is zero, say 'at rest'.

Segment C is stage 3: the train covers more track each second, so the curve grows steeper: speeding up.

Segment D is stage 4: less track each second, so the curve flattens into the 10 m mark: slowing down.

Behind every one of those readings is one fact: the slope of a position-time graph at a moment is the velocity at that moment, sign included. A straight segment keeps one slope, so one velocity. A curve's slope keeps changing, so the velocity keeps changing.

Read the shape: flat means at rest; straight sloped means constant velocity; a steepening curve means speeding up; a flattening curve means slowing down.

The graph shows a paraglider's position. Which of these describes the paraglider's motion during segment K?

K is straight, so its slope is constant: constant velocity.

Falling only sets the sign of that velocity. It does not mean slowing down.

During segment K the paraglider moves at constant velocity.

The graph shows a mail cart's position. Which of these describes the cart's motion during segment T?

The graph shows a canoe's position. Which of these describes the canoe's motion during segment M?

M curves, so its slope is changing: the velocity is changing.

The curve flattens as it rises, so the slope's size falls: the canoe is slowing down.

During segment M the canoe is slowing down.

The graph shows a car's position leaving a depot. Which of these describes the car's motion during segment U?

Steeper-means-faster works for falling segments too. A falling curve that steepens shows something speeding up in the negative direction.

Your turn

The graph shows a hawk's position along a valley. Which of these describes the hawk's motion during segment W?

The graph shows a cargo boat's position approaching a dock. Which of these describes the boat's motion during segment Z?

The graph shows one journey with four labeled segments. During which segment is the object slowing down?