Scalar & Vectors

Definition of a scalar:     A quantity with size (magnitude) only.
Examples: speed, distance, time, mass, volume, work done, pressure, energy, power and density.

Definition of a vector:    A quantity with size (magnitude) and direction.
Examples: displacement, velocity, force, weight, gravitational field strength and acceleration.

Displacement is the vector alternative for distance and is defined as distance moved in a particular direction. Velocity in turn is the vector alternative for speed and is defined as speed in a stated direction.

 

Take the following example:

Tom and Amy are taking a walk in the park. They follow the winding pathway and walk a total of 500m. Their distance is 500m, however their displacement is only be 300m west to east.

Path taken

 

 

Distance = 500m
Displacement = 300m from west to east
Note that all vector quantities can be positive or negative depended on direction.

 

Some fundamental equations

Speed = Distance
                 Time                                                                      

Where  Speed (m/s or ms^-1)
Distance (m)
Time (s) 

Acceleration = Change in Velocity
                              Time Taken                   

Where  Acceleration (ms^-2)
Change in Velocity (ms^-1)
Time Taken (s)