Then you must have table in your home. It has Length with the parameters like mas. The length is measured in units of Meter. Yes. Most of us wake up or try to wake up in the morning with help of alarm bell of clock. The clock tells us time in unit of seconds.

In many cases, the temperature is measured in units of kelvin, the other quantity like Luminous Intensity has unit candela, The electric current is measured in units of ampere and quantity of matter in moles.

Let us summarize what we have mentioned in above paragraphs: kilogram,, metre, second, kelvin, candela, ampere, mole. These 7 units are known as Fundamental units. Why fundamental units, because all these units are independent of each other.

There are 2 supplementary fundamental units also. One is radian and other steradian of quantities of plane angle and solid angle respectively.

Derived units:

Those units which are derived from fundamental units are known as derived units. It means they depend upon fundamental units. For example, units of area is metre square. Unit of speed is metre per second, unit of acceleration is metre per second square.

This is all about the difference between fundamental units and derive units.

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Let us think about many things that you feel, observe or see during your daily routine. You woke with a sound of alarm. Thus, basically what is sound, how it reaches your ear is again the branch of Physics that is known as Acoustics.

Let us take another example, why sky is blue? This is again due to a wonderful phenomenon of nature that is Scattering.

If someone got fracture and how to diagnose it. Of course, many times with X rays and many times a serious disease with MRI. This is again Physics.

How astronauts travel to space. By using many applications pf Physics like gravity etc.

How light travels, this is studied by another branch pf Physics that is Optics.

How water is used to generate electricity, how wind mills run, how solar energy trapped and generate electricity, and there are so many examples of Physics and its applications.

On the basis of these applications, Physics may be broadly divided into following types but not limited to this only:

1. Mechanics
2. Optics
3. Energy
4. High Energy
5. Relativity
6. Electrodynamics
7. Superconductivity
8. Nuclear Physics
9. Particle Physics
10. Quantum Physics
11. Semiconductor Physics
12. Astronomy
13. Acoustics
14. Thermodynamics
15. Condensed matter Physics

Thus, there are so many applications of Physics. One can say that many applications, equations, concepts of Mathematics, chemistry, biology are originated from Physics.

This is all about Physics, a beautiful branch of Science. Please share the examples of Physics that you observe in your daily life in comments section. Thanks.

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Definition of displacement: Displacement is the shortest path between the two points. It must be the straight line and straight line is always the shortest path. Velocity is related with displacement and it is defined as rate of change of displacement.

Definition of Angular displacement: As the name suggests, this type of displacement must be in rotation. It is normally represented by θ.

Angular velocity is related with angular displacement. It is represented by rate of change of angular displacement. It is normally represented by ω that is ω = dθ/dt.

These are the differences between displacement and angular displacement and their relations with velocity and angular velocity respectively.

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The question here is can a object has acceleration when its velocity is zero. You will be surprised to know that there are certain cases where this can happen. Let us discuss 2 of the examples:

1. When you through a ball upside and when it reaches the top it pauses for a moment. At this moment, the velocity is zero but the ball still has acceleration and that acceleration is due to acceleration due to gravity. Thus at the peak, the velocity is zero but the object is still accelerating.

2. Second example can be discussed in the case of pendulum. When a pendulum moves, and when it reaches the extreme positions its velocity is zero but its still accelerating due to gravity.

It means there may be cases where acceleration may be there even if there is no velocity.

If you know more examples,  you can share with us.

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Suppose a body has an initial velocity u and is moving with uniform acceleration a.

Let the final velocity of the body after time t = v.

a = dv/dt

Or                                                              dv = adt                                               …(i)

When‘t’ = o; velocity = u

When‘t’ = t; velocity = v

Integrating equation (i) between these limits, we have

∫dv = ∫adt

(a is uniform i.e. constant)

Or                                                                    [v]^v_u = a[t]^t_o

Or                                                                    v – u = a (t – o) = at

Or                                                                          v = u + at                        ….(ii)

This is the relation between velocity and acceleration. This is also the relation between initial velocity, final velocity and acceleration.

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Acceleration: The state of change of velocity of a body with time is known as its acceleration.

If the velocity of a body increases with time, then its acceleration is positive. On the other hand, if the velocity of a body decreases with time, then its acceleration is negative. Negative acceleration is also called retardation or deceleration. Acceleration is a vector quantity.

Units of acceleration. The units of acceleration are:

Cms^-2 in the CGS system

And                                          ms^-2 in the MKS system or SI units

Average Acceleration. When a body is moving with variable acceleration, then its average acceleration in a given interval of time is defined as the ratio of the change in velocity of the body to the time interval.

If v1 is the velocity of the body at time t₁ and v2 is the velocity of the body at time t₂, then its average acceleration during the time interval (t₂ – t₁) is given by.

a = v2 – v1/t2 – t1

Uniform Acceleration. A body is said to be moving with uniform acc. if its average acc. between any two points along its path is the same in magnitude as well as direction.

Or

A body is said to be moving h uniform acceleration if its velocity changes by equal amounts in equal intervals of time, however small these intervals may be.

Variable Acceleration. A body is said to be moving with variable acceleration if its average acceleration is different between different points along its path, either in magnitude or in direction or both in magnitude as well as direction.

Or

A body is said to be moving with variable acceleration if its velocity changes by unequal amount in equal intervals of time, however small these intervals may be.

Instantaneous Acceleration. When a body is moving with variable acceleration, then its acceleration at a particular instant of time or at a particular position along its path is known as its instantaneous acceleration It is equal to the limiting value of average acceleration as Dt tends to zero, which shows that the instantaneous accelration of a body is equal to the first derivative of velocity or the second derivative of displacement w.r.t time.

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Velocity: The time rate of change of position of a body in a particular direction is known as its velocity.

Or

The time rate of change of displacement of a body is known as its velocity.

i.e.                                            Velocity = displacement/time

Velocity is a vector quantity. It can be positive negative or zero as displacement can be +ve, -ve or zero.

Units of velocity: Units of velocity are the same as those of speed.

i.e.                                            cm s^-1 In the CGS system

And                                          ms^-1 In the MKS system or SI units

Average velocity: Suppose a body is moving along a straight line (say along x-axis). Let

Displacement of the body in time t₁ =

Displacement of the body in time t₂ = x1

Displacement of the body in time t₂ – t₁ =  x2

The value of x2 – x1 depends upon the time interval (t₂ – t₁)

Let t₂ – t₁ = dt and  x2-x1= dx

Now, average velocity of a body is defined as the ratio of the linear displacement of the body to the time taken in undergoing this displacement.

Uniform velocity: A body is said to be moving with uniform velocity if its average velocity between any two points along its path is the same in magnitude as well as direction.

Or

A body is said to be moving with uniform velocity is it always moves in the same direction and covers equal distances in equal intervals of time, however small these intervals may be.

Variable velocity: A body is said to be moving with variable velocity if its average velocity is different between different points along its path either in magnitude or in direction or both in magnitude as well as direction.

Or

A body is said to be moving with variable velocity if it covers distances in unequal intervals of time or unequal distances in equal intervals of time, however small these intervals may be, or it changes its direction of motion.

Instantaneous velocity: When a body is moving with variable velocity, then its velocity at a particular instant of time or at a particular point along its path is known as its instantaneous velocity. It is equal to the limiting value of average velocity  as dt tends to zero.

Instantaneous velocity is equal to the differential coefficient of displacement w.r.t time.

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But there are other terms also like uniform speed, variable speed, average speed, and instantaneous speed also.

Let us discuss the definitions of speed, uniform speed, variable speed, average speed, and instantaneous speed and try to understand the difference between them in the following section:

1. Speed: The time rate of change of position of a body in any direction is known as its speed.

It is measured by the ratio of the distance by a body to the time in which this distance is covered

i.e.                                                        Speed = distance/time

Speed is a scalar quantity. It is either positive or zero but never negative.

Units of speed: We know that,

Speed = Distance/Time

Units of speed = Units of distance/Units of time

In the CGS system, a unit of speed is cms-1, and in the MKS system or SI units, the unit of speed is ms^-1.

2. Uniform Speed: A body is said to be moving with uniform speed if it covers equal distances in equal intervals of time, however small these intervals may be. For example, if a body starts at 5 pm and move till 6 pm and covers 60 KM. If body covers 10 Km in first 10 minutes then 10 KM in next 10 minutes and so on. It means body covers equal distances in equal intervals of time.

3. Variable Speed: A body is said to be moving with variable speed if it covers unequal distances in equal intervals of time, however small these intervals may be. In the above example, if the body covers 10 Km in the first 10 minutes then 12 Km in the next 10 and then 8 in the next 10, and so on. It means the body is covering unequal distances in equal intervals of time.

4. Average Speed: Average speed of a body is defined as that uniform speed with which it covers the same distance in a given interval of time as is actually covered by it in the same interval of time while moving with variable speed.

It is given by the ratio of the total distance traveled by the body to the total time taken by it.

i.e.                                Average speed =Total distance traveled/Total time taken

5. Instantaneous Speed: When a body is moving with variable speed, then, its speed at any instant of time is known as its instantaneous speed.

If a body travels a very small distance Ds in a very small interval of time Dt, then its

Instantaneous speed = limit time tends to 0(ds/dt)

Numerical: Try to solve the following numerical and share your answer in the comments section:

If a car travels at a uniform speed of 60 Km per hour in first 40 minutes and then 70 KM per hour in next 30 minutes. Calculate the average speed.

I hope you have understood the difference between speed, uniform speed, variable speed, average speed, and instantaneous speed.

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1. Distance: The actual length of the path covered by a body in moving from one position to another is called distance traveled by the body. Suppose you move in a square shaped ground (each side 100 m) from east to west, then from west to east at the same point. The total distance covered will be 200 m. It is a scalar quantity. It is measured in centimeters (cm) in the CGS system and in metres (m) in the M.K.S system or SI units. The distance covered by a body in motion can never be zero or negative.

2. Displacement: Displacement of an object in a given interval of time is defined as the change in its position in a particular direction during that time. It is the shortest or the straight line distance between the initial an the final positions of the object.

In the above mentioned example of square ground, the total displacement is zero.

Displacement is a vector quantity. It is represented by an arrow with its tail at the initial position and head at the final position of the object. The length of the arrow gives us the magnitude of displacement and the arrow head gives its direction. For example, if an object moves from A to C along the path ABC, then its displacement is . The arrow head at C indicates that the object is displaced from A to C.

It should be noted that the distance covered by a body may be more than its displacement. For example, if a body moves from its initial position A to the final position B along a zig-zag path as shown in the figure, then the distance covered by the body is more than its displacement.

Similarly if a body is moving in a circle of radius r, then distance covered by the body in none rotation = 2pr but displacement of the body in one rotation = zero

Characteristics of displacement:

(i) The unit of displacement is the same as that of length.

(ii) The displacement of a body in a given time interval can be positive, negative or zero.

(iii) Displacement is a vector quantity.

(iv) The magnitude of displacement of a body between two points gives the shortest distance between these points.

(v) The displacement of a body does not depend upon the choice of origin.

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1. Motion in one dimension:

The motion of a body is said to be in one dimension or one –dimensional motion if it moves along a straight line in any direction. This type of motion is also called rectilinear or linear motion. Only one position co-ordinate is required to describe the position of the particle in this motion.

Examples (i) Motion of a vehicle on a straight line.

(ii) Motion of a train on a straight railway track.

(iii) Motion of an object dropped from a certain height from the ground.

(iv) A man working on a straight path etc.

2. Motion in two dimensions

The motion of a body is said to be in two dimensions or two dimensional motion if it moves ordinates are required to describe the motion of the particle.

Examples: (i) Motion of an insect on a floor

(ii) Motion of a boat in a river

(iii) Motion of earth around the sun

(iv) Motion of a shell fired from a gun

(v) Motion of a billiard ball on the billiard tale etc.

3. Motion in three dimensions: The motion of a body is said to be in three dimensions or three dimensional motion if it moves in space. In this type of motion three position co-ordinates are required to describe the position of the particle.

Examples: (i) Motion of a kite

(ii) Motion of an aeroplane

(iii) Motion of a flying bird

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