Speed-time graphs

The confusing thing is that SPEED-Time graphs often ‘look’ the same as DISTANCE-Time graphs. But they are very different and the information you can read from them is also very different. Let’s start with the basics. The axes look like this …

stg1

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. Here we will use hours. Sometimes the times are written as ‘clock’ times, e.g. 9am – 10am – 11am, or 1300 – 1400 – 1500 etc.

Speed – the units here could be in centimetres per second (cm/s), metres per second (m/s), or kilometres per hour (km/h). Again it depends on the type of journey. Usually, for journeys by car, bus, train or plane, kilometre per hour (km/h) are used. However, pay great attention to the question because it may ask for a speed in kilometres per hour but the units on the SPEED axis may be in metres per minute, or even per second. And you must know how to convert from one to the other.

Let’s use an example…

You get on a train at 10 am. Starting from rest the train takes 15 minutes to reach a speed of 70 km/h. It stays at this speed for another 15 minutes and then during the next 30 minutes its speed reaches 110 km/hour. The train stays at this speed for another 15 minutes but, because the driver must stop at the next station, the train begins to steadily slow down. It takes the train 30 minutes to steadily slow down and come to a stop at the next station platform.

Now what would all this information look like on a SPEED-Time graph?

Well what do we know?

The whole journey takes 105 minutes (1 hour 45 minutes).

This is just adding up all the little bits of time given.

The fastest speed reached is 110 km/h.

So the SPEED axis will probably not go beyond 120 km/h

From rest the train took 15 minutes to reach 70 km/h.

This ‘From rest’ tells you that the graph must begin with the SPEED at ZERO and Time at ZERO – in other words, at the Origin. In the first 15 minutes its speed steadily increased from 0 km/h to 70 km/h (the red line)

It stayed at 70 km/h for the next 15 minutes.

So there was no change in the speed for 15 minutes – so this must be a ‘flat’ part of the graph (the blue line).

Then, over the next 30 minutes, its speed increased from 70 to 110 km/h.

An increase in speed means the graph will rise ( ).

It stays at 110 km/h for the next 15 minutes.

Again another ‘flat’ part of the graph ( ).

During the last 30 minutes the train steadily slows down and comes to a stop.

After travelling at 110 km/h for 15 minutes, the train now takes 30 minutes to steadily slow down to zero speed ( ).

Now let’s put all of this information onto a SPEED-Time graph……

stg2

stg3

So remember, the gradients of straight lines in a SPEED-Time graph are values telling you how fast the speed is changing – they are ACCELERATIONS.

But…

– Lines with POSITIVE gradients are ACCELERATIONS – they tell you how fast the speed is INCREASING.

– Lines with NEGATIVE gradients are DECELERATIONS – they tell you how fast the speed is DECREASING.

Also notice I have used the word ‘steadily’ when describing the changing speeds.

This is because the lines are straight. In the real world, of course, speeds don’t usually change in a steady way – you speed up a bit, slow down a little, speed up a bit more etc. So the value of a straight-line gradient on a SPEED-Time graph is really an AVERAGE acceleration.

Now we come to the other important information that can be found in a SPEED-Time graph – DISTANCES!

Just take a look at this rectangle under the speed-time graph ……

stg4

Let’s find its AREA…..(and pay great attention to the UNITS)….

stg5

In other words, the total AREA under a SPEED-Time graph is the total DISTANCE travelled during the journey. And this is very often a question in IGCSE – find the total distance travelled. Let’s see how we would do this for our SPEED-Time graph.

Basically chop it up into easy bits – rectangles and triangles – and then find the area of each bit and add them up. Like this…..

stg6

So,

Total distance travelled between 10 am and 11:45 am is….

= 8.75 km + 17.5 km + 35 km + 10 km + 27.5 km + 27.5 km

= 126.25 km

Points to remember:

  • Positive gradients of straight lines are ACCELERATIONS.
  • Negative gradients of straight lines are DECELERATIONS.
  • Lines with no gradient (‘flat’) are times of CONSTANT speed.
  • AREAS beneath SPEED-Time graphs are DISTANCES travelled.