1. Introduction
The properties of vectors which have been discussed in the previous
sections can all be applied to physical quantities which are vectors. In
general, all physical quantities which require a magnitude and a
direction in order to be fully described are vectors. Such physical
quantities are distinguished from scalar quantities which have magnitude
only.
2. Distance and displacement
DISPLACEMENT is a vector quantity which represents the difference in the position of two points. It is given the symbol s and has units of metres (m) in a specified direction.Displacement must be distinguished from the scalar quantity DISTANCE, which has the units of metres. The difference between distance and displacement is illustrated by the following problem:

Answer: The displacement of the valve from the man is 10 m North, which is twice the radius of the circular tank).The minimum walking distance is halfway around the tank, which is π x radius = 3.14 x 5 (m) = 15.7 m.
3. Speed and velocity
SPEED is a scalar quantity defined as the RATE OF CHANGE OF DISTANCE. The units of speed are metres per second (m·s-1).The AVERAGE SPEED, v, may be calculated by dividing the distance travelled, Δx, by the time taken, Δt, to cover the distance, for example,

VELOCITY is a vector quantity defined as the RATE OF CHANGE OF DISPLACEMENT. It is given the symbol v and has units of metres per second (m·s-1) in a specified direction. AVERAGE VELOCITY may be defined as the total displacement divided by the time taken to make that displacement, that is, v = Δx/Δt.
Instantaneous velocity is defined in a similar way to that of instantaneous speed).
4. Acceleration
ACCELERATION is a vector quantity defined as the RATE OF CHANGE OF VELOCITY. It is given the symbol a and it has units of meters per second squared (m·s-2).AVERAGE OF ACCELERATION, a is calculated by dividing the change in velocity Δv that occured during a time interval, Δt, by that time interval Δt. For example, if the velocity of an object changed from 3 m·s-1 to 5 m·s-1 in 5 seconds, then the average acceleration can be calculated:

Objects in motion undergo acceleration if either the speed or the direction of motion changes. Motion in which the direction does NOT change is called RECTILINEAR MOTION (i.e., the object moves in a straight line - see here what is meant by non-rectilinear motion). If the instantaneous acceleration is the same throughout a given time interval, then the object is said to be UNIFORMLY ACCELERATED. In this case, the velocity changes by equal amounts in equal intervals of time.
If a body which has an initial velocity, vi, undergoes an acceleration a for a time Δt, we can see from the definition of acceleration that the final velocity vf will be given by vf = vi + aΔt
If the acceleration is UNIFORM, then the average velocity, v, over the time interval is:


5. Experimental determination of s, v and a
In school experiments the change in displacement, velocity, and
acceleration of bodies in rectilinear motion can be measured as a
function of time by attaching the bodies to a paper tape and having the
tape passing through a ticker timer:


The change in displacement of the object as a function of time can be measured directly from the tape. (The experimenter must choose the origin appropriately).
The average velocity of the object in a time interval can be calculated by measuring the change in displacement during the interval and dividing it by the time interval:


6. Force
If a coiled spring is stretched or compressed, it is said that a force is acting on the spring.


Since force has a magnitude and a direction, it is a vector. The unit of force is the NEWTON (N) in a specified direction. A force of 1 N on a mass of 1 kg will cause that mass to accelerate at 1 m·s-2:

If several forces, not in equilibrium, act on a body, the force which is required to produce equilibrium is called the EQUILIBRANT: