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Distance-time graphs

Forces and motion · level 4, lesson 3 of 6

A question to start

The team on Earth gets back a record of the rover's drive: how far it had gone at each moment. How can a picture of that record show at a glance when the rover was moving fast, slowly, or not at all?

The idea

A distance-time graph puts time along the bottom and distance up the side. Each point says how far the rover had gone at that time.

  • A straight sloping line means a steady speed.
  • A steeper line means a faster speed.
  • A flat line means the distance is not changing: the rover is stopped.
  • The speed is the slope: how much the distance goes up, divided by how much time passes.
205080time, minutes 6090metresstopped

The graph shows a drive in three parts: 60 m in the first 20 minutes, a stop of 30 minutes to take pictures, then 30 m more in 30 minutes.

Worked examples

1. Part one. \(60 \text{ m} \div 20 \text{ min} = 3\) m per minute, which is 0.05 m/s.

2. Part two. Flat: speed zero, the rover is stopped for \(50 - 20 = 30\) minutes.

3. Part three. \((90 - 60) \text{ m} \div (80 - 50) \text{ min} = 1\) m per minute: a gentler slope, a slower speed.

4. Average speed for the whole drive. Total distance over total time: \(90 \div 80 = 1.1\) m per minute. Lower than either moving part, because of the stop.

Try it

  1. On a distance-time graph, what does a flat line mean?
  2. Which is faster: a steep line or a gentle one?
  3. A line rises from 0 m to 120 m in 40 minutes. What is the speed in m per minute?
  4. A rover drives 30 m in 10 min, stops for 20 min, then drives 30 m in 10 min. What is its average speed?
Answers
  1. The thing is not moving.
  2. The steep one.
  3. \(120 \div 40 = 3\) m per minute.
  4. \(60 \text{ m} \div 40 \text{ min} = 1.5\) m per minute.

Common mistake

Reading a distance-time graph as a map. A line going up does not mean the rover is climbing a hill. It means its distance from the start is growing. A flat line is not flat ground; it is a stop.

Where it leads