Now that you understand the difference between vectors and scalars, we will have a look at two important examples of these, namely speed and velocity, in more detail.
The definition of speed is:
The best way to imagine a situation in which several physical quantities are changing, is by drawing a graph. To picture the behaviour of the speed of an object, we plot the distance (from the top of the equation for speed) on the vertical axis and the time (from the bottom of the equation for speed) on the horizontal axis. The result is something like this:
Here, the total distance travelled (y) divided by the time taken (x) is the gradient of the slope. This is also equal to the average speed of the object  remembering that
In this case, the speed is constant as the slope of the distancetime graph is constant.
By rearranging the equation we can plot slopes of either distance, or time, on a graph to find their values. For example, we can see how to find the distance from a speedtime graph by rearranging to get:
We then plot a speedtime graph as shown below:
The blue rectangle has an area equal to the speed multiplied by the time. We can see from the equation above that this is equal to the distance travelled.
Displacement is a vector quantity that describes a distance moved, in a particular direction. The change in an object's displacement with time is called velocity:
We can produce a displacementtime graph to illustrate an object's velocity. Study the following example of a displacementtime graph.

The graph below describes the motion of an ice hockey puck travelling in a straight line and at a constant speed towards the goal.
Here, the velocity of the ice hockey puck is given by:

As before, we can rearrange the equation, using the two quantities, on the same side of the equation, as axes, to find out the quantity on the other side.
Now you have all the skills required to try these examples involving motion at constant speed or velocity.
Apollo 11, the first spacecraft to land people on the Moon, took 102 hours to reach its destination. The average speed of the craft was 5500 km/h. What is the distance to the Moon?
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During training, a player runs the 100m length of a football pitch in 20s, stops for 10s and jogs back in 35s. Draw a displacementtime graph for this activity from its starting point. What is the player's total displacement? What is the velocity (in the direction of the first stage run) at each of the three stages?_{}

