When we observe our surroundings, we can see many physical interactions taking place around us like a book falling, an ear drum vibrating, bus moving, nuclear reactions etc. Everything in the universe moves. It can either be a small amount of movement or swift, but movement does happen this change in position of an object is called Motion.
If an object is moving, we would be curious to know what are the things happening that make a body move, how long will a body move and many other queries pop in.
To understand the importance of Motion we have a clear example mentioned below:
An object tends to continue in its motion at a constant velocity until and unless an outside force acts on it. The term velocity refers both to the speed and the direction in which an object is moving. It is easy to recognize an object in motion and an object at rest. One must apply an external force to disrupt the balance.
The following are the terms to be recognized before learning Motion:
Rest: When the body does not change its position with respect to the surroundings, the body is said to be at rest.
Motion and Rest are relative terms. For example: The person sitting inside the moving train is at rest, whereas the person sitting next to him but who is at Motion with the person outside the moving train.
A book on the table is at rest with respect to the table and other objects in the room. But all these objects are sharing the motion of the earth
Or
A car moving on a road is said to be in motion compared to the poles and trees on the roadside. But the people sitting inside the car are at rest compared to one another.
Motion is a change in position of an object or else a process of moving or being moved. When the body changes its position with respect to its surrounding, the body is said to be in Motion.
Examples: Football on ground, motion of moon around earth, rock falling off a cliff, a car moving on the road to trees on the roadside, person inside a moving bus with respect to person outside the bus, bird flying in sky are the examples of motion.
The minimum distance between two points is called
displacement while the actual path covered is called distance. The
displacement is a vector term and distance is scalar term. Distance and
displacement both have SI unit as meter.
$AB + BC$ = distance moved and $AC$ = displacement
The effect of $AB + BC$ is same as effect of $AC$.
On one round trip, distance is $2(AB + BC)$ while the displacement = $AC + CA$ = $0$
Hence the distance is never zero while the displacement is zero in one round trip.
As we know that the rate of change of displacement is velocity similarly we have,
$Speed$ = $\frac{Distance\ moved}{Time\ taken}$
$S$ = $\frac{d}{t}$
where $d$ is distance moved.
The $SI$ unit for velocity and speed is meter/second $(m/s)$.
The speed is scalar term and velocity is vector term.
The speed cannot be zero since distance cannot be zero while the velocity can be zero as displacement can be zero.
a) Uniform motion: When equal distance is covered in equal interval of time, the motion is said to be in uniform motion. The bodies moving with constant speed or velocity have uniform motion or increase at the uniform rate.b) Non Uniform motion: When unequal distances are covered in equal interval of time, the motion is said to be in non uniform motion. The bodies executing non uniform motion have varying speed or velocity.We can even classify motion into three types:
Translatory motion
Rotatory motion
Vibratory motion
Translatory Motion
In Translatory motion, the particle moves from one point in space to another. This motion may be along a straight line or along a curved path.
They can be classified as:
Rectilinear Motion: Motion along a straight line is called rectilinear motion.
Curvilinear Motion: Motion along a curved path is called curvilinear motion.
Rotatory Motion
In Rotatory motion, the particles of the body describe concentric circles about the axis of motion.
Vibratory Motion
In Vibratory motion, the particles move to and fro about a fixed point.
The variable quantities in a uniformly accelerated rectilinear motion
are time, speed, distance covered and acceleration. Simple relations
exist between these quantities. These relations are expressed in terms
of equations called equations of motion.
Consider a particle moving along a straight line with uniform acceleration '$a$'. At $t$ = $0$, let the particle be at $A$ and $u$ be its initial velocity and when $t$ = $t$, $V$ be its final velocity.
Average Velocity = Average Velocity = .....(1) Average Velocity can be written as Average Velocity = ........(2) From equations (1) and (2) = .......(3) The first equation of motion is $v$ = $u + at$.Substituting the value of $v$ in equation (3) we get
Consider an object moving with a uniform velocity u in a straight line. Let it be, given a uniform acceleration at time, t = 0 when its initial velocity is u. As a result of the acceleration, its velocity increases to v (final velocity) in time t and s is the distance covered by the object in time t. The figure shows the velocity-time graph of the motion of the object.
Slope of the v - t graph gives the acceleration of the moving object.
Thus, acceleration = slope = AB = $\frac{BC}{AC}$ = $\frac{v - u}{t - 0}$ a = $\frac{v - u}{t}$
v - u = at
v = u + at................................................................(1)
Second Equation of Motion
Let u be the initial velocity of an object and 'a' the acceleration produced in the body. The distance traveled s in time t is given by the area enclosed by the velocity-time graph for the time interval 0 to t.
Distance traveled s = area of the trapezium ABDO
= area of rectangle ACDO + area of Î”ABC
= OD x OA + $\frac{1}{2}$ BC x AC
= t x u + $\frac{1}{2}$ (v - u) x t
= ut + $\frac{1}{2}$ (v - u) x t
(v = u + at I eqn of motion; v - u = at) S = ut + $\frac{1}{2}$at x t S = ut + $\frac{1}{2}$at^{2}.
Third Equation of Motion
Let 'u' be the initial velocity of an object and a be the acceleration produced in the body. The distance travelled 's' in time 't' is given by the area enclosed by the v - t graph.
The graph of straight line parallel to the
X axis shows that the body is moving with constant velocity.
b)For uniform motion: This graph shows the equal displacement in equal interval of time so, the slope = $\frac {\Delta Y} {\Delta X}$ gives the change in position over corresponding change in time is constant. Thus, this graph shows the uniform motion.
c) For Body at Rest:
The position-time graph parallel to time axis shows that the body is at rest. d) For Non uniform motion:
This graph shows unequal distance in
equal interval of time which gives the change in
position over corresponding change in time which is varying.
Motion can be angular or uniform. When
the body moves on a curved path, there is a change in angular
displacement, this is called an angular motion. The rate of
change of angular displacement gives angular velocity. It’s
a vector term. The angular motion is always an accelerated motion.
Speed = $\frac{Distance\ moved}{Time\ taken}$ S = $\frac{d}{t}$
where, d is distance moved.
The SI unit for velocity and speed is meter/second (m/s). The speed is scalar term and velocity is vector term. The speed cannot be zero since distance cannot be zero while the velocity can be zero as displacement can be zero. → Read More
Newton has given the three laws of motion.Newton’s First law of motion: The body remains in rest or in continue
motion unless some external force is applied on it. Example: The book on
table will remain on table unless some force is applied on it. The ball
moving on ground stops by itself because of friction (external
force). If there were no frictional forces, the moving ball will
continue to move unless we stop it.
First law of motion is related to term “Inertia”. It’s the property of
body by the virtue of which the body resists the external force.
Common examples of inertia in our day to day life:
The passengers fall forward when the bus suddenly stops. This is due to
inertia of motion, the lower portion of body comes to rest but the upper
portion of body continue to be in motion.
When we shake the branches, the fruits and leaves fall. The branches are
in motion while the fruits and leaves are in rest so, they fall.
The dust particles get removed when we shake the carpet. This is, because
the particles are at rest while the carpet is moving, so, the particles are removed.
When the person jumps from the moving bus, he runs through some distance due to inertia of motion.
Any moving body has momentum. Mathematically, the momentum is denoted by P. It’s the product of mass and its velocity. P = mass x velocity P = m x v
Newton’s Second law of motion: According to the Newton’s second law of
motion the rate of change of momentum is directly proportional to the force
applied and acts in the direction of force.
F = $\frac{dP}{dt}$ ……………………………….(1)
dP is change in momentum
F = d $\frac{(mv – mu)}{dt}$……………………(2)
m = mass of body.
F = m $\frac{d(v - u)} {dt}$
$\therefore$ F = ma …………………….(3)
a = $\frac{v – u}{t}$
Force = mass x acceleration
Hence, a = $\frac{F}{m}$
For constant force, acceleration produced in the body, is inversely proportional to the mass of the body. Larger is mass, lesser is acceleration produced.
For equal masses of the body, the acceleration is directly proportional to the force applied. Larger is force, higher is acceleration produced. Newton’s Third law of motion: To every action, there is an equal and opposite reaction.
Common examples of Newton’s third law in our day today life:
When a person jumps from a boat, the boat moves backwards.
When a bullet is fired, the gun goes backwards.
The huge amount of smoke downward, pushes the rocket upwards.
When a balloon is blown, the air rushes outward while the balloon moves backward with the same momentum.