Motion is the change in position of an object with respect to its
surrounding in a given interval of time. Atoms, molecules, planets, stars
and galaxies all are in motion.
Most motions are complex, some object may move in a straight line others
may take a circular path. Some may rotate and few may vibrate.
Motion along a straight line
It is the simplest form of motion, when an object moves along a straight
line. Moving from a point A to a point B in a straight line representing
different position at different time is said to be the motion of an object
in a straight line. The magnitude of the motion is given by a numerical
value.
Distance
It is the total path covered by an object while moving from a particular
point to another point.
Displacement
It is defined as the shortest distance between two point measured while
moving from the initial position to the final position.
Uniform motion
An object is said to be in a uniform motion when it covers equal distance
in equal interval of time. The time interval in this motion may be small or
big. Suppose an object travels 50 kilometre in fast hour and another 50
kilometre more in the second hour, then the object can be said to be in a
uniform motion.
Non-uniform motion
An object is said to be in a non-uniform motion when the distance covered
by it is unequal in equal interval of time. When a car moves in a crowded
traffic then it have to start and stop at different position at different
point of time. Which makes the movement of the car unequal in equal
interval of time.
Rate of motion
The rate of motion can be defined as the total distance travelled by an
object in a particular span of time. The rate of motion is also termed as
the average speed of an object. The average speed of an object is defined
as total distance travelled divided by total time taken. The standard unit
of motion is metre per second.
Speed with direction
The rate of motion of an object can be more comprehensive defined when we
specify its direction of motion along with its speed. The quantity
specifying both these aspects is called velocity.
The average velocity of an object can be defined as the summation of the
initial velocity and the final velocity divided by 2. The unit of velocity
is the same as the unit of speed that is metre per second.
Rate of change of velocity
In case of uniform motion the velocity remains constant with time. But in
case of non-uniform motion velocity varies with time. It has different
values at different instant of time and at different points of path. To
measure that change in velocity another physical quantity is introduced
that is called acceleration. Acceleration can be defined as the change in
velocity divided by the total time taken.
SI unit of acceleration is metre per second square.
Uniform acceleration
A free falling body is an example of uniformly accelerated motion. Where
the velocity increases in equal amount in equal interval of time.
Non uniform acceleration
An object travelling along a straight line increases its speed by unequal
amount in equal interval of time is said to have a non uniform
acceleration.
Graphical representation of motion
Distance time graph
The change in the position of an object with time can be represented on the
time distance graph adopting a convenient scale of choice. In this graph
time is taken along x-axis and distance is taken along y-axis. When the
plotting of time and distance in the graph is a straight line at an angle
of 45 degree the motion of that object is uniform.
From the graph, we can reduce that distance travelled by an object is
directly proportional to the time taken. From the graph we can calculate
the average speed of an object from a particular point of time to another
point of time.
Velocity time graph
The variation in velocity with time for an object moving in a straight line
can be represented by a velocity time graph. In this graph, time is
represented along x-axis and velocity is represented along the y-axis. In
this graph, when an object moves with a uniform velocity the height of the
velocity time graph will not change with time.
Equation of motion
When an object moves along a straight line with uniform acceleration, it is
possible to relate its velocity, acceleration during motion and the
distance covered by it in a certain time interval by a set of equation
known as the equations of motion.
Equations:
Equation for velocity time relation
Considering the velocity time graph of an object that is in acceleration.
We see that the initial velocity of an object is u and then it increases to
v in time t. The velocity changes at a uniform rate a. From these variables
equations can be derived from velocity time relation.
Equation for position time relation
An object has travelled a distance s in time t under
uniform acceleration a. Then the distance travelled by the object
is given by:
Equation for position velocity relation
From the velocity-time graph, the distance s travelled by the object in
time t, moving under uniform acceleration a is given by:
Uniform circular motion
When an object moves in a closed path then the object is said to be in a
circular motion. In the case of a circular motion an object does not change
its magnitude of velocity but the direction of motion is changed
continuously. A closed path is not necessary to be a circle, it can be
rectangular, hexagonal, octagonal or circular path.
When an object moves along the circumference of a circle of radius r. Then
the velocity v of that object can be determined by 2πr divided by time.
We can observe that when we rotate a stone tied with a string with our hand
and suddenly release it, the stone moves along a straight line tangential
to the circular path. So, from this we can say of the stone was
continuously changing its direction.