# test3

In this module, you will learn about distance and displacement.

\textbf{Concept of coordinate system:}

Everyday , we see lots of things moving around. For example a vehicle is
passing through from one place to other. In scientific terms, an object
is said to be in motion, if it changes its position with time; and at
rest if it does not change its position with time.

A coordinate system, shown below, consisting of three mutually
perpendicular axes, labelled X-, Y-, and Z- axes is used to locate the
position of an object in motion or at rest. The point of intersection of
these three axes is called origin and denoted as ‘O’. The coordinates
(x, y. z) of an object describe the position of the object with respect
to this coordinate system.

\textbf{\textit{Figure:1.a}}

To measure time , a clock is introduced in the coordinate system.. The
coordinate system along with the clock constitutes a \textbf{Frame of
reference}.

To describe motion along a straight line, an axis, say X-axis can be
taken, so that it coincides with the path of the object. Positions to
the right of origin O are taken as positive and to the left of O, as
taken as negative. This is also applicable for Y-axis. This is shown
below.

\textbf{\textit{Figure:1.b}}

\textbf{Distance and displacement:}

Consider, an object is at position A at time t$_{1}$ and at position
B at time t$_{2}$.

\textbf{\textit{Figure:1.c}}

In the time interval between t$_{1}$ to t$_{2}$, the object has
travelled a path ACB to reach at B. The length of the path ACB is known
as the \textbf{distance} travelled by the object in the time interval
t$_{1}$ to t$_{2.}$

Now if the initial position A and the final position B are connected by
a straight line, a shortest path length is obtained. This shortest path
between two positions is called displacement.

Displacement of an object has both magnitude and direction. The
magnitude of displacement is equal to the length of straight line
joining initial and final positions; and its direction points from the
initial position towards its final position.

\textbf{\textit{Figure:1.d}}

So, displacement is defined as the change in position of an object.

If $x_{1}$ and $x_{2}$ are the positions of an object at time $t_{1}$ and $t_{2}$, then the displacement in time $\Delta t=t_{2}-t_{1}$ is given by $\Delta x =x_{2}-x_{1}$.

Let’s look at the below examples to understand displacement in detail.

Example 1: An object travels from P to Q, then Q to R, R to S and then
comes back to P. The total path covered i.e. the distance travelled is =
6+2+6+2 = 16 m.

As the object comes back to the initial position P, therefore the
displacement of the object is zero.

\textbf{\textit{Figure:1.e}}

Example 2: An object travels from A to B, then to C as shown below.

\textbf{\textit{Figure:1.f}}

The distance travelled by the object 4 + 3 = 7 m.

As the displacement is the shortest path between the initial and final
points, therefore, the displacement of the object is AC = 5 m and its
direction is from A to C.

Example 3: An object moves from point A to point D through B, C and E.

\textbf{\textit{Figure:1.g}}

\newcounter{numberedCntB}

1. Calculate the final displacement.
\setcounter{numberedCntB}{\theenumi}

The final displacement of the object = final position – initial position
= 3 – 1 = 2 m.

\setcounter{enumi}{\thenumberedCntB}
1. Calculate the distance travelled from point A to C.
\setcounter{numberedCntB}{\theenumi}
Distance travelled from A to B = 5 – 1 = 4 m

Distance travelled from B to C = 4 – 1 = 3 m

So, total distance travelled = 4 + 3 = 7 m

\textbf{Position-Time graphs (General representation of motion of
object):}

\newcounter{numberedCntA}

1. Object is at rest:
\setcounter{numberedCntA}{\theenumi}

\textbf{\textit{Figure:1.h}}

b. Object is in uniform motion:

If an object covers equal distances in equal intervals of time, it is
said to be in uniform motion.

\textbf{\textit{Figure:1.i}}

\begin{center}\textbf{INDEX}\end{center}

Coordinate system 1

Direction 3-4

Displacement 2-5

Magnitude 3

Origin 1

Position 1-5

Frame of reference 1

Uniform motion 6