2.09 One Dimensional Motion

Objects can move along any path in 3 dimensions (e.g a path that combines some forward/backward, left/right and up/down movement). However we will restrict our analysis initialy to objects which are moving in just one dimension. i.e. motion along a straight line. This results in the following simplifications.

As the motion is along a straight line there are only two possible directions.
These can be represented with plus (+) and minus (-) signs.
(E.g (+) = up and (-) = down or (+) = right and (-) = left etc.)
(Note we don't always have to write the plus sign as we assume a number is positive unless indicated otherwise with a minus sign!)
Because distance will now be restricted to a straight line (like displacement) then unless a moving object changes direction the magnitude of its displacement will be equal to the distance travelled and speed would be equal to the magnitude of the object's velocity.
This point is illustrated by the examples below

Example 1
In 10 seconds an object travels 20 meters from a reference point
Over this period
total distance = 20m
Total displacement is +20m
The magnitude of the displacement is equal to the distance so speed will be equal to the magnitude of velocity
(s = 20/10 = 2 ms^-1, v = 20/10 = 2 ms^-1)

Example 2
In 5 seconds an object travels 2 meters from a reference point before changing direction and then moving 3 metres in the opposite direction
Over this period
total distance = 5m
Total displacement is -1m (2-3)
The magnitude of displacement is not equal to the distance so speed will not be equal to the magnitude of velocity
(s = 5/5 = 1 ms^-1, v = -1/5 = -0.2 ms^-1)

Instantaneous values

We assume there can be no change of direction during the very short interval used to calculate and instantaneous values
Therefore for one dimension motion the magnitude of instantaneous velocity = instantaneous speed
(note : even though the speed is equal the magnitude of the velocity it still differs from velocity as it has no information about direction)
e.g. if instantaneous velocity is +3 ms^-1 speed is 3 ms^-1.
However if velocity is -3 ms^-1 speed is still 3 ms^-1 )