# Travel Graphs

Then come back and try this question. Click on the graph to make it bigger. There’ll almost certainly be something like this in IG.

When speed is constant (in other words the speed doesn’t change) we find it as shown:

Speed = distance travelled
time taken

so: time taken = distance/speed and distance = speed x time

Remember, when using any formula, the units must all be consistent. For example speed could be measured in m/s, distance in metres and time in seconds.

If speed does change, the average (mean) speed can be calculated:

Average speed = total distance travelled
total time taken

Example:
If a car travels at a speed of 10m/s for 3 minutes, how far will it travel?
Firstly, change the 3 minutes into 180 seconds, so that the units are consistent. Now rearrange the first equation to get distance = speed × time.
Therefore distance travelled = 10 × 180 = 1800m = 1.8km

Units
In calculations, units must be consistent, so if the units in the question are not all the same (e.g. m/s, m and s or km/h, km and h), change the units before starting, as above.

The following is an example of how to change the units:

Example:
Change 30km/h into m/s.

30km/h = 30/60 km/min              (1)

= 30/3600 km/s = 1/120 km/s     (2)

= 1000/120 m/s = 8.33 m/s        (3)

In line (1), we divide by 60 because there are 60 minutes in an hour. Often people have problems working out whether they need to divide or multiply by a certain number to change the units. If you think about it, in 1 minute, the object is going to travel less distance than in an hour. So we divide by 60, not multiply to get a smaller number.

Next: the reverse process

Change 20m/s into km/h

20m/s = 20x60x60m/h

Divide by 1000 to convert the m into km:

20m/s = 72km/h

Velocity and Acceleration

Velocity is the speed of a particle and its direction of motion (therefore velocity is a vector quantity, whereas speed is a scalar quantity).
When the velocity (speed) of a moving object is increasing we say that the object is accelerating. If the velocity decreases it is said to be decelerating. Acceleration is therefore the rate of change of velocity (change in velocity / time for change) and is measured in m/s².

Example:
A car starts from rest and within 5 seconds is travelling at 20m/s. What is its acceleration?

Acceleration = change in velocity / time for change = 20/5 = 4m/s2

Distance-time graphs:
These have the distance from a certain point on the vertical axis and the time on the horizontal axis. The velocity can be calculated by finding the slope or gradient of the graph.

The slope = RISE (how far up) / RUN (how far along)

Velocity-time graphs/ speed-time graphs:
A velocity-time graph has the velocity or speed of an object on the vertical axis and time on the horizontal axis. The distance travelled can be calculated by finding the area under a velocity-time graph. Acceleration is the gradient or slope of a velocity-time graph.

On travel graphs, time always goes on the horizontal axis (because it is the independent variable).

Vectors have size and direction, scalars have size only