Motion and speed
In a nutshell
The speed of an object tells you how fast it is travelling. By looking at the relationship between distance and time, you can find out the speed of an object and sometimes even the way in which the speed of the object is changing.
Equations
WORD EQUATION  SYMBOL EQUATION 
$speed = \frac{distance}{time}$  $s = \frac{d}{t}$ 
Variable definitions
QUANTITY NAME  SYMBOL  UNIT NAME  UNIT 
$speed$  $s$  $metre \space per \space second$  $m/s$ 
$distance$  $d$  $metre$  $m$ 
$time$  $t$  $second$  $s$ 
Speed calculations
You can find the average speed of the object if you know the distance it has travelled and the time it took for the object to travel that far.
$speed = \frac{distance}{time}$
$s = \frac{d}{t}$
If you need to calculate the distance travelled instead, you can rearrange this equation to make distance the subject. Or if you need to find the time taken to travel a certain distance, you can rearrange for time.
Example
A car travels at a speed of $3 \space m/s$ for a total of $10 \space seconds$. How far has the car travelled in metres?
Begin by writing out the quantities you been given:
$speed = 3 \space m/s$
$time = 10 \space s$
Rearrange the equation to find distance travelled:
$distance = speed \times time$
Substitute the values into the equation:
$distance = 3 \times 10$
The distance travelled by the car is $\underline{30 \space m}$.
Distancetime graphs
A distancetime graph shows you how the speed of an object changes over time. Distance is plotted on the $x$axis and time is plotted on the $y$axis. The slope, also called the gradient, tells you the speed of the object. The shape of the distancetime graph can also tell you about how the motion of the object is changing.
1.  If a distancetime graph has a straight line section, it means that the object is moving with a constant speed. If it is uphill, then the object is moving away from the starting point. If it is downhill, then the object is moving back towards the starting point. The steeper the straight line, the faster the object is moving.

2.  If a distancetime graph has a flat section, it means that the object has stopped moving. 
3.  If a distancetime graph has a curve in it, then this means that the object is changing speed. If it is a steeping curve, then the object is getting faster or, in other words, accelerating. If it is a curve that is levelling off, then the object is slowing down or decelerating. 