definitions / instantaneous and average velocity
Definitions
Some important definitions are shown in the table below:
Quantity 
Symbol 
Definition 
Example 
SI Unit 
Vector or Scalar 
Displacement 
s or r 
The distance moved in a particular direction. 
The displacement from London to Rome is 1.43 x 10^{6} m southeast. 
m 
vector 
Velocity 
v or u 
The rate or change of displacement

The average velocity during a flight from London to Rome is 160 ms^{1} southeast. 
ms^{1} 
vector 
Speed 
v or u 
The rate of change of distance.

The average speed during a flight from London to Rome is 160 ms^{1} . 
ms^{1} 
scalar 
Acceleration 
a 
The rate of change of velocity.

The average acceleration of a plane on the runway during takeoff is 3.5 ms^{2} in a forwards direction. This means that on average, its velocity changes every second by 3.5 ms^{1} . 
ms^{2} 
vector 
These technical terms should not be confused with their everyday use. In particular you should note that:

vector quantities always have a direction associated with them.

generally, velocity and speed are NOT the same thing. This is particularly important if the object is not going in a straight line.
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Instantaneous and Average Velocity
The average value of velocity over a period of time is very different to the instantaneous value at a particular instant in time.
Imagine a sprinter during a 100 m race where the sprinter covered the distance in 11.3 seconds. The average speed over the whole race is easy to work out. It is the total distance (100 m) divided by the time (11.3 s) giving 8.5 ms^{1}.
During the race, however, her instantaneous speed would have changed. If at the end of 2.0 seconds she had travelled 10.4 m, here average speed for the first two seconds would have been 10.04/2.0 = 5.0 ms^{1}. During these first two seconds her instantaneous speed was increasing  she was accelerating. If she started at rest and her average speed over the whole 2 s was 5.02 ms^{1} then her instantaneous speed at 2 s must be more than this. In fact, the instantaneous speed for this sprinter was 9.23 ms^{1} at 2 s, but it would have been impossible to work this out from the information given.
You can use the following website to see an animation showing the difference between average speed and instantaneous speed.
http://www.physicsclassroom.com/mmedia/kinema/trip.html
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download worksheet 8.4.1.A  kinematics
download experiment 1  measuring speed 