Analysis of Straight Line Motion with Constant Velocity -...

Analysis of Straight
Line Motion with
Constant Velocity

Purpose
The purpose of this experiment is to prove that any object moving without any net
force acting over it does so in a straight line and with constant velocity, and to calculate this
velocity.
Introduction
A continious change of position of an object in time is called motion. Motion is
classified into several types, with the simplest taking place in a linear path with constant
velocity. No net force acts on the object in this particular type of motion. In this experiment,
this theory will be proven.
Theory
As mentioned above, the type of motion we are dealing with (straight line motion with
constant velocity) takes place under two conditions; when the object is not stationary (when it
is already moving) and when the net force applied to the object is zero. According to
Newton’s First Law of Motion, a stationary object will remain at rest, and an object moving
on a linear path will keep doing so unless a net force is applied to the object in question.
In order to express this physical law mathematically, the objects are assumed to be
point particles. The moving object will have a position vector R , which will be defined by the
use of a stationary reference frame (being the observer’s frame of reference, in this
experiment). This vector will be defined as a function of time, since this position vector will
be different at each given time. The average of the differences of the position of the object at
different times along predefined time intervals will be its average velocity.
In this case, however, since we are working in one dimension (an arbitrarily taken x-
axis), we shall express the position vector in one dimension as well. Furthermore, since there
will not be a net force acting over the object, there will not be any positive or negative
acceleration. Therefore, this calculated average velocity will be also equal to the

instantaneous velocity of the object (which is the rate of change of position of an object in a
given instant) at any given time in which the motion occurs.
These formulae could also be derived using derivatives. Since the derivative of a
function yields its rate of change, the derivative of the position vector function will give the
object’s average velocity function.