Distance-time graphs

  • Do you know the difference between a ‘Distance-Time’ graph and a ‘Speed-Time’ graph?
  • Do you know what different information you can get from each types of graph?
  • Do you know what the ‘gradient’ of the straight, sloping lines mean in each type of graph?

Let’s see …

Let’s suppose you cycle from your house to a friend’s house 10 km away. Let’s suppose it takes you 1 hour to get there because, for most of the way, it’s uphill, and let’s suppose you stay for an hour. You then cycle back home but, because it’s now downhill, the homeward journey only takes you 30 minutes.

What would this look like on a ‘Distance-Time’ graph?

  • Time always goes along the bottom horizontal axis.
  • Distance always on the vertical axis.

dtg1

Distance time graphs – diagram 1

Always pay careful attention to the UNITS!

Time – the units here could be in seconds, minutes, hours, even days (depending on the journey). But usually, for everyday-type journeys, hours are used. In this example we will use hours. Sometimes the times are written as ‘clock’ times, e.g. 9am – 10am – 11am, or 1300 – 1400 – 1500 etc.

Distance – the units here could be in centimetres, metres or kilometres (again it depends on the type of journey). Usually kilometres (km) are used.

dtg2

So what do we know?

We know

  • It takes 1 hour to get to your friend’s house which is 10 km from your house. But where does the graph start? Obviously at your house. And how far are you from your house at the start? At the very beginning of your journey you have ZERO distance from your house. So the graph must start at (0,0) – the Origin, (this is the red line below).
  • You stay at your friend’s house for 1 hour. If you are at your friend’s house you must be 10 km from your house, and if you ‘stay’ for 1 hour, your distance from your house cannot change. So this part of the graph will be a flat line for the 1 hour you are in your friend’s house, (the blue line ).
  • It takes you 30 minutes to cycle home. The moment you leave your friend’s house and head for home, the distance you are from home must begin to get less and less. When you finally reach your house the distance you are from your house is again ZERO – so you have come back down to the Time axis,(the green line ).

dtg3

 

dtg4

 

dtg6

Some points to remember………

So the steepness (gradient) of the straight, sloping lines, tells you the speed – BUT because these lines are straight what they are really saying is the speed was CONSTANT. Now, of course, in real life this never happens – especially on a bicycle! There are traffic lights, hills, punctures, winds – all of which can affect your speed. So when we calculate the speed from the gradient of a straight line what we are actually describing is the AVERAGE speed for that part of the journey.

Use the units on the axes! Do NOT measure the Rise and Run with a ruler! The value of the gradient depends entirely on the scale and the units on the two axes. You MUST understand how each axis is scaled (do they go up by 1’s, or 2’s, or 5’s, or 10’s etc?) and use the units when dividing the Rise by the Run.