Speed and Velocity
REST AND MOTION
Rest: When position of a body does not change with time it is said to be in state of rest.
Motion: When position of a body changes with time it is said to be in state of motion. Rest and motion are relative terms.
(i) Absolute motion: The motion of a body with respect to a body which is at complete rest is called absolute motion which is impossible.
(ii) Relative motion: The motion of a body with respect to a body which is at rest relative to the body is called relative motion.
MOTION IN ONE, TWO AND THREE
DIMENSIONS
Motion in One Dimension
An object moving along a straight line or path is said to have dimensional motion, also known as rectilinear motion.
Examples Motion of a bus on a straight road and motion of a train on a straight track, an object dropped from a certain height above the ground, etc.
Motion in Two Dimensions
An object moving in a plane is said to have two dimensional motion,
Examples: Motion of an insect on a floor, earth revolving around the sun, a billiard ball moving over the billiard table, etc.
Motion in Three Dimensions
An object moving in space is said to have three dimensional motion
Examples: Motion of a Kite. motion of a flying aeroplane or bird, etc.
POSITION, PATH LENGTH AND
DISPLACEMENT
Position
The position of any particle can be given as follows:
In cartesian co-ordianate form: The position of any particle is resented by co-ordinates (x, y, z) or position vector\[(\overrightarrow{r})\]. If a particle is located at point A in frame of reference x, y, z then the position of particle will be
\[\overrightarrow{r}=x\,\hat{i}+y\,\hat{j}\,+z\,\,\hat{k}\]
In polar form: \[x=r\cos \theta ;\,\,y=r\sin \theta \]
\[\overrightarrow{r}=r\cos \theta \,\hat{i}\,+r\sin \theta \,\hat{j}\]
Path Length or Distance
The length of the actual path between initial and final positions of a particle in a given interval of time is called distance covered by the particle. Distance is the actual length of the path. It is the characteristic property of any path i.e. path is always associated when we consider distance between two positions.
Characteristics of distance
(i) It is a scalar quantity
(ii) It depends on the path
(iii) It never reduces with time.
(iv) Distance covered by a particle is always positive and can never be negative or zero.
(v) Dimension: \[\left[ M{}^\circ LT0 \right]\]
(vi) Unit: In C. G S. centimetre (cm), in S.I. system, metre (m).
Displacement
The shortest distance from the initial position to the final position of the particle is called displacement

Position vector of Aw.r.t. O=\[\overrightarrow{OA}\]
\[\Rightarrow \] \[\overrightarrow{{{r}_{A}}}={{x}_{1}}\,\,\hat{i}+{{y}_{1}}\,\,\hat{j}+{{z}_{1}}\,\,\hat{k}\]
Position vector of B w.r.t. O\[=\overrightarrow{OB}\]
\[\Rightarrow \] \[\overrightarrow{{{r}_{B}}}={{x}_{2}}\,\,\hat{i}+{{y}_{2}}\,\,\hat{j}+{{z}_{1}}\,\,\hat{k}\]
Displacement \[=\overrightarrow{AB}=({{x}_{2}}-{{x}_{1}})\,\,\hat{i}+({{y}_{2}}-{{y}_{1}})\,\,\hat{j}+({{z}_{2}}-{{z}_{1}})\,\,\hat{k}\]
\[\Delta \overrightarrow{r}=\Delta x\,\,\hat{i}+\Delta y\,\,\hat{j}+\Delta z\,\,\hat{k}\]
Characteristics of displacement
(i) It is a vector quantity.
(ii) The displacement of a particle between any two points is equal
more...