# There and back

Let us at first look at a simple uniform motion.
A mass point moves along a linear path according the shown time-distance-graph.

Is it possible to specify the related graph for the speed in an explicit way?

1. a) Yes (try it with a sketch)
2. b) No

Does a movement like this occur in nature?

1. b) Yes
2. b) No

The answer for the first question is: a) Yes.

The (average) velocity (=speed and its direction) v of a body is defined as a change in position, a displacement Ds in a certain time interval Dt. As units result for example m/s or km/h.

The movement starts at 0 meter and goes on steadily to the position 6 meter after 3 seconds.

Then it returns in the same way back to the starting point. This is called a uniform linear motion.

The speed on the forward way is 6 meter/3 seconds or 2 m/s.
On the way back accordingly (minus) – 2 m/s.

The answer for the second question is: b) No.

In nature the reversion of motion after 3 sec at 6 m never happens immediate, i.e. without any delay (0 sec). The moved mass has to be slowed down to 0 m/s and then be accelerated to – 2 m/s. This cannot go on infinitely fast, as this would mean an infinitely great force.

Besides that no body is absolutely rigid, but deformable. Thus forces always will be “absorbed” to some degree.

The above shown abrupt reversal of velocity is therefore an idealization. In reality it runs according to the rounded curve sketched at the right.