Class 9 Science

Equation of Motion

  • First equation of motion
  • Second equation of motion
  • Third equation of motion

Relation among velocity, distance, time and acceleration is called equations of motion. There are three equations of motion, viz. first, second and third equations of motion. In this part, you will learn about mathematical derivation of equations of motion.

First Equation of Motion

The final velocity (v) of a moving object with uniform acceleration (a) after time, t.

Let, the initial velocity = u.
Final velocity = v.
Time = t
Acceleration = a

We know that, Acceleration (a) `=(text{Change in velocity})/(text{Time taken})`

`=> a=(text{Final velocity-Initial velocity})/text{Time taken}`

`=>a=(v-u)/t`

`=>at=v-u`

`=>at-v=-u`

`=>-v=-u-at`

`=>v=u+at` ---(i)

This equation is known as first equation of motion.

Second Equation of Motion

Distance covered in time (t) by a moving body.

Let, Initial velocity of the object = u
Final velocity of the object = v
Acceleration = a
Time = t
Distance covered in given time = s

We know that,

Average velocity `=(text{Initial velocity+Final velocity})/2`

∴ Average velocity `=(u+v)/2` ----(ii)

We know that, Distance covered (s) in given time = Average velocity x Time

Or, s = Average velocity x Time -----------------(iii)

After substituting the value of average velocity from equation (ii) we get

`=>s=(u+v)/2xxt`

After substituting the value of ā€˜vā€™ from first equation of motion we get,

`=>s=(u+(u+at))/2xxt`

`=>s=(u+u+at)/2 xxt`

`=>s=(2u+at)/2 xxt`

`=> s=(2ut+at^2)/2`

`=>s=(2ut)/2+(at^2)/2`

`=>s= ut+(at^2)/2`

`=>s=ut+1/2 at^2` ----(iv)

The above equation is known as Second equation of motion.

Third Equation of Motion

The third equation of motion is derived by substituting the value of time (t) from first equation of motion.

We know from first equation of motion, `v=u+at`

`=>v-u=at`

`=>at=v-u`

`=>t=(v-u)/a` -----(v)

We know that the second equation of motion is, `s=ut+1/2at^2`

By substituting the value of `t` from euqation (v) we get

`s=u((v-u)/a)+1/2a((v-u)/a)^2`

`=>s=uxx(v-u)/a+1/2a((v-u)^2)/a^2`

`=>s=(u(v-u))/a +(axx(v-u)^2)/(2xxaxxa)`

`=>s=(uv-u^2)/a + ((v-u)^2)/(2a)`

`=>s=(2(uv-u^2)+(v-u)^2)/(2a)`

`=>2as=2uv-2u^2+v^2+u^2-2uv`

`=>2as=-2u^2+v^2+u^2`

`=>2as=-u^2+v^2`

`=>2as+u^2=v^2`

`=>v^2=u^2+2as` ---(vi)

This is called the Third equation of motion.


Matter in Our Surroundings

Anything that has both mass and volume is called matter. You can also say that anything which has mass and which occupies space is called matter.

Is Matter Around Us Pure?

Elements and compounds are pure substances. All other substances are mixtures which means they are not pure substances.

Atoms and Molecules

Read about law of conservation of mass, law of constant proportions and Dalton's atomic theory.

Structure of Atoms

Atom is made of three particles; electron, proton and neutron. These particles are called fundamental particles of an atom or sub atomic particles.

Cell: The Fundamental Unit of Life

A cell is capable of independent existence and can carry out all the functions which are necessary for a living being.

Tissue

A groups of cells which is meant for a specific task is called tissue. Tissues are the first step towards division of labour in complex organisms.

Diversity in Living Organisms

Without proper classification, it would be impossible to study millions of organisms which exist on this earth.

Motion

If an object changes its position with respect to a reference point with elapse of time, the object is said to be in motion.

Force & Laws of Motion

Force has numerous effects. Force can set a stationary body in motion. Force can stop a moving body.

Gravitation

Earth attracts everything towards it by an unseen force of attraction. This force of attraction is known as gravitation or gravitation pull.

Work & Energy

When force is exerted on an object and object is displaced, work is said to be done. It means work is the product of force and displacement.

Sound

Sound is a type of energy. Sound travels in the form of wave from one place to another.

Why Do We Fall Ill

Health is a state of physical, mental and social well being. A condition in which the affected person is unable to carry out normal activities is termed as disease.

Natural Resources

Resources which are obtained from nature are called natural resources. Examples: Air, water, soil, wood, etc.

Improvement in Food Production

Food security is said to exist when all people, at all times, have physical and economic access to sufficient, safe and nutritious food to meet their dietary needs and food preferences for an active and healthy life.