Force And Motion

Distance and displacement

Distance :- Any path covered by an object is known as distance. It’s SI unit is meter (m). It is a scalar quantity.

Displacement :- The shortest distance between initial and final position of a moving body in a particular direction is known as displacement. It’s SI unit is meter (m). It is a vector quantity.

Differences between distance and displacement

Distance	Displacement
It is any path covered by an object.	It is shortest distance between initial and final position.
It is a scalar quantity.	It is a vector quantity.
It is always positive.	It can be positive, negative or zero.

Speed and velocity

Speed:- The rate of change of distance is known as speed. It’s SI unit is m/s. It is a scalar quantity.

Uniform speed:- If an object covers equal distance in equal interval of time then it is said to be in uniform speed.

Non-uniform speed:- If an object does not covers equal distance in equal interval of time then it is said to be in Non-uniform speed.

Velocity:- The rate of change of displacement is known as velocity. Its SI unit is m/s. It is a vector quantity.

Uniform velocity: – If an object covers equal displacement in equal interval of time then it is said to be in uniform velocity.

Non-uniform velocity:-If an object do not covers equal displacement in equal interval of time then it is said to be in Non-uniform velocity.

Difference between speed and velocity

Speed	Velocity
It is a rate of change of distance.	It is a rate of change of displacement.
It is a scalar quantity.	It is a vector quantity.
It is always positive.	It may be positive, negative or zero.

Acceleration and retardation

Acceleration :- The rate of change of velocity is known as acceleration. It is denoted by letter ‘a. Its SI unit is m/s^2.It is a vector quantity.

If the velocity of any object changes from initial velocity (u) to final velocity (v) in time (t). Then

Acceleration = (final velocity – initial velocity)/time

a=(v-u)/t

Negative acceleration is known as retardation.

Inertia

Inertia is defined as a property of matter by which it remains at the state of rest or in uniform motion in the same straight line unless acted upon by some external force.

Relation between inertia and mass:- Inertia directly depends on a mass of a body that means greater the mass greater will be the inertia. Thus, lighter body has less inertia than heavier body. For example, It is easier to push an empty bucket than to push a bucket full of water. The bucket full of water has greater inertia as compared to empty bucket.

Types of inertia

Inertia of rest:- Inertia of rest is the tendency of a body to remain in its state of rest or its inability to change its state of rest by itself.

If any matter is at rest it will continue to remain at rest unless an external force is applied to change its state of rest. This property of body is called the inertia of rest.

Example

When a bus starts suddenly , the passengers sitting in the bus falls backward: When a passenger sitting in a stationary bus, both the bus and passenger are at rest. When the bus starts suddenly lower parts of the passenger’s body starts to move with bus but upper parts of the passenger’s body tends to remain in the state of rest due to inertia of rest. That’s why passenger tends to fall backward.

Inertia of motion:- Inertia of motion is the tendency of a body to remain in its state of motion or its inability to change its state of motion by itself.

If any matter is in a state of motion, it will continue to remain at motion unless an external force is applied to change its state of motion . This property of body is called the inertia of motion.

Example

When a running bus stops suddenly, the passengers are jerked forward: In a running bus the speed of the passenger is equal to the speed of bus. As the bus stops suddenly lower parts of the passenger comes to rest but the upper parts of the passenger tends to remain in motion due to inertia of motion. That’s why passenger jerked forward.

Newton's laws of motion

Newton’s first law of motion:- It states that “Everybody in this universe will remains in state of rest or state of uniform motion in a straight line unless an external force is applied on it”.

Newton’s second law of motion:- It states that “Acceleration produced on a body is directly proportional to force applied and inversely proportional to mass of a body”. Therefore,

a α F ………….. (i)

a α 1/m ………….. (ii)

Combining equation (i) and (ii)

a α F/m

ma α F

F α ma

F = K ma …………. (iii)

Where, K is proportionality constant.

As we know that , 1 N force is defined as force required to produce acceleration of 1 m/s² on a body of mass 1 kg.

So, if m = 1 kg and a = 1 m/s²then F = 1 N.

Therefore equation (iii) becomes

1 = K 1.1

or, K = 1

Substituting the value of K = 1 in equation (iii)

F = 1 ma

F = ma

Newton’s third law of motion:- Newton,s third law of motion states that “To every action, there is an equal and opposite reaction”.