A scalar quantity only has magnitude
This is
just a numerical quantity (or size), usually with units), but
no specific direction.
Examples:
Speed, distance, mass, time,
temperature (K or oC), potential difference (V), current (A).
Non of these automatically
implies the use of direction.
However if you apply a direction
to speed or distance, it becomes a vector quantity.
A vector quantity has both magnitude
(size) and
specific direction.
Examples:
Velocity (m/s),
is the rate of change of
position in a specific direction (compare with speed above)
(you can think of velocity as
'speed in a particular direction', but take care in how you use the
words speed and velocity!)
Acceleration (m/s2),
is the rate
of increase in velocity/speed in a specific direction
Momentum
(kg m/s)
the product of the mass x velocity of an object moving in a
particular direction.
Displacement
(m) is
the distance an object has moved in a particular direction.
Force
(N) is also considered to act in a specific direction.
ALL
forces are vector quantities
They all have a magnitude, and, at
any point, act in a specific direction.
e.g. electrostatic
(attraction/repulsion), gravitational, magnetic, (attraction/repulsion) pushing, pulling, tension,
compression.
On diagrams vector quantities are
usually depicted with an arrow, the length of the arrow can show the
magnitude and the angle of the arrow shows the direction along
which the quantity acts.
In the diagram above, you have two
cyclist travelling at the same speed of 2 m/s, but in opposite
directions. Therefore, although they have the same speed
(same length of arrow), they have different velocities because
they are travelling in different directions. Note that the velocity of
the left cyclist is formally given a negative sign to indicate the
opposite direction of motion (it doesn't mean going slower or slowing
down!).
Diagrams illustrating force
vectors
Two forces acting on an object.
The length of the arrows are
proportional to the magnitude of the forces involved - in this case two
acting forces and a resultant force.
One force is acting to the right and
the other to the left (blue arrows).
The net force, resultant force, is
acting to the right - do you see its a simple logical calculation?
Which is net force to the right =
780 - 330 = 450 N
Lots more on resultant forces on
this page and also on
Calculating resultant forces using vector
diagrams
1.
2.
3. 
A parachutist and parachute
These diagrams show the relative
magnitude of the two forces acting on a descending parachutist.
Note the relative size and direction of
the arrows. The weight force F2 is constant.
1. When the parachutist opens the
parachute, there is an immediate large drag force due to big increase in
air resistance (air friction).
2. As the parachutist slows down (decelerates) the air
resistance (F1) reduces and continues to do so until F1 = F2.
3. When drag force F1 equals the
weight force F2 (arrows of equal length), the parachutist is descending
at a steady speed - a terminal velocity.
Remember the drag force on an object
due to friction (air resistance), increases with speed i.e. as more air
brushes over the surface of the object in the same time.
This parachute situation is fully
explained on the
Acceleration,
friction, drag effects, terminal velocity page
