Motion
Introduction
State (State of a body)
- Rest
- Motion
Physical quantities and sytem of a unit
Distance and displacement
Speed, Velocity
Average speed and average velocity
Uniform and non uniform motion
Accleration
Uniform and non uniform acceleration
Equation of motion
Circular motion
Graphical representation of motion
In physics there are two state of an object
1- Rest/Stationary
2- Motion
Rest/stationary state of an object
An object is said to be in rest when at does not change its position with the respect of their surrounding.
In rest state an object has fixed position
Ex- tree , house , electric pole , factory etc.
Motion state of an object
An object is said to be in motion when its position changes continuously with respect to a stationary object taken as reference point.
It the phenomenon in which an object changes its position with respect to tire.
Ex:-flying birds, rotating planets, swimming fishes
Physical quantities
All those quantities which can be measured is called physical quantities
Ex:- length, mass, time, temperature, force, pressure, work
There are two types of physical quantities
1- scalar quantities
2- Vector quantities
Scalar quantities
Those quantities whose magnitude is fixed but direction is not fixed are called scalar quantities. They are are not dependent on direction, they can described only by magnitude.
Ex:- length, mass, time, temperature, density etc.
the symbol of scalar quantities are represented simply
ex_ distance - d
time - t
Vector quantities
Those quantities whose magnitude and direction both are fixed are called vector quantities. They are dependent on both direction as well as magnitude.
Ex:- force
the symbol of vector quantities are represented by an arrow.
System of units
those tools which can be used to measure the physical quantities effectively is called system of unit. They are standardized value so that they are acceptable in every country.
Measurement of physical quantities are expressed in terms of unit which are standardized value.
-SI system-
International system of unit-
The international system of units (SI) is the metric system that is used universally as a standard for measurements.
It is used universally in technical and scientific research to avoid the confusion with the units. It is important because it helps the entire world to understand the measurement in one set of unit systems.
Name of quantity SI. unit SI. unit symbol
Length meter m
Mass kilogram kg
Time second s
Electric current ampere A
Thermodynamic temperature Kelvin K
Amount of substance mole Mol
Luminous intensity candela cd
The SI system is made of seven base units and these seven base units are used to define twenty two derived units.
The seven base units are:-
1- meter (m)
2- second (s)
3- Ampere (A)
4- Mole (Mol)
5- Kilogram (kg)
6- Kelvin (K)
7- candela (cd)
There are three types of system of units:-
1- MKS
2- CGS
3- FPS
Distance and displacement
Distance is the actual length of the path by a moving body irrespective of the direction in which the body travels.
Total distance = 4km + 2km + 8km
It is a scalar quantity Distance is represented by 'd'
- Displacement-
The shortest distance between the initial position and final position of the body along with direction is known as displacement.
Note :- The symbol by which initial position represents are 'pi'. The symbol by which final are 'pf'.
Displacement is represented by the symbol 's'
:. s = pf - pi
Calculate the Displacement in given figure.
Calculate the distance and displacement in given figure.
Note:- Distance never becomes zero but sometimes displacement becomes sometimes zero.
What is the displacement of a car when it moving around a circular park when final position and initial position are same.
Is displacement becomes zero on straight path.
Describe speed?
Ans:- Speed of the body is the distance traveled by the body in per unit time. It gives an idea of how slow or fast that body is moving. Speed is a scalar quantity as it has only direction and no magnitude.
Speed is measured as the ratio of distance to the time in which the distance was covered.
∴ S = d / t
;.ijlwhere S = speed in m/s
d = distance traveled in m
t = time taken in second
The SI unit of speed is m/s
The unit of speed in CGS system is cm/s
There are four types of speed.
1- Uniform speed-An object is said to be in uniform speed when the object covers equal distance in equal time intervals.
Ex:- rotation of earth, revolution of earth, pendulum etc.
2- Variable speed- An object is said to be in variable speed when the object covers a different distance at equal interval of time.
3- Average speed- Average speed is defined as the uniform speed which is given by the ratio of total disntance travelled by an object to the total time taken by the object.
4- Instantaneous speed- When an object is moving with variable speed, than the speed of that object at any instant of time is known as instantaneous speed.
Explain Velocity
The distance traveled by a body in per unit of time in a given direction is called velocity of the body. Velocity is a vector quantity as it has magnitude as well direction. Velocity gives an idea of direction of motion.
Velocity of a body is the displacement produced per unit of time
∴ velocity = distance traveled in a given time / time taken
→ ∴ V = Displacement / time
→ ∴ V = change in position in a particular direction / time
→ ∴ V = Pf – Pi /t
The SI unit of velocity is m/s
Numerical-1
A car travels a distance of 100 km in 2 hr. Calculate speed of the car.
Numerical-2
A car travels a distance of 100 km in east in 2 hr. Calculate speed of the car.
Numerical-3
A boy goes to the soap that is 100m far from his home and return to the home back in 40 second. find its speed.
Numerical-4
A boy goes to the soap that is 100m far from his home and return to the home back in 40 second. find its velocity.
Uniform / Non-uniform motion
Uniform motion:- When a body travels equal distances in equal intervals of time. than the motion of the body is called uniform motion. In uniform motion the speed of the object is constant.
Non-Uniform motion:- When a body travels unequal distances in equal intervals of time. than the motion of the body is called Non-uniform motion. In Non-uniform motion the speed of object is not constant.
or
When a body travels equal distances in unequal intervals of time. than the motion of the body is called Non-uniform motion.
Average speed and average velocity
The total distance traveled by the object in a particular interval of time is called average speed.
Average speed = Total distance covered / total time taken
∴ Average speed = d1 +d2 + d3 + d4 / t1 + t2 + t3 + t4
Numerical -4
An object travels 16 m in 4 seconds and then another 16m in 2 seconds. What is the average speed of the object.
Solution:- d1 = 16 m t1 = 4s
d2 = 16 m t2 = 2s
total distance = d1 + d2 = 16m + 16m = 32m
total time taken = t1 + t2 = 4s + 2s = 6s
average speed = total distance covered / total time taken
= 32m / 6s = 5.33 m/s
Average velocity
The change in displacement divided by the time intervals in which the displacement occurs is called average velocity. It is the ratio of the total displacement to the total time taken by the object.The average velocity can be negative or positive depending upon the sign of the displacement. The SI unit of the average velocity is m/s.
Average velocity = total displacement / total time
If the velocity is changing but at uniform rate, than the average velocity will be the arithmetic mean of initial velocity and final velocity.
∴ Average velocity = initial velocity + final velocity / 2
Numerical-5
Usha swims in a 90m long pool. She covers 180m in one minute by swimming from one end to other and and back along the same straight path. Find the average speed and average velocity of Usha.
Solution:- Total distance covered by usha in 1 min = 180m
Displacement of usha in 1 min = 0m
∴ Average speed = total distance covered / Total time taken
= 180m /1m = 180m / 60 sec = 3m/s
∴ Average velocity = Total displacement / total time taken
= 0m / 60sec = 0m/sec
Hence, Average speed of usha = 3m/sec and Average velocity of usha = 0m/sec
Numerical - 6
An object has moved through a distance. Can it have zero displacement? If yes, support your answer with example.
Ans:- Yes, an object which has moved through a distance can have zero displacement if it comes back to initial position.
Ex:- If a person jogs in a circular park which is circular and complete one round . His initial and final position is same.
Than his displacement is 0
Numerical-7
A farmre moves along the boundry of a square field of side 10m in 40 seconds. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial point.
Solution:- Rounds covered in 40 seconds = 1
∴Rounds covered in140 seconds = 1/40 ✕ 140
= 3.5 rounds
= 3full rounds and 1 half round
In the 3 full rounds displacement = 0 ( because initial and final position are same )
But in next half round displacement =
(AC)2 = (AD)2 + (DC)2
(AC)2 = (10)2 + (10)2
(AC)2 = 100 + 100
(AC)2 = 200
AC = √200
AC = 14.143m
Which of the following is true for displacement?
(a) It cannot be zero
Solution- false
(b) Its magnitude is greater than the distance travelled by the object.
Solution - false
Distinguish between speed and velocity
|
Speed |
Velocity |
|
The rate at which an object covers a certain distance is known as speed. |
The rate at which an object changes position in a certain direction |
|
Speed cannot be negative or zero. |
It can be negative or zero. |
|
Speed is a scalar quantity. |
It is a vector quantity. |
|
Speed = distance / time |
Velocity = displacement / time |
Under what conditions is the magnitude of average velocity of an object equal to its average speed?
Solution:- Only when the object moves along a straight line path.
What does the odometer of an automobile measure?
Solution:- It measures distance travelled by the vehicle.
What does the path of an object look look like when it is in uniform motion.
Ans:- Uniform motion = equal distance covered in equal intervals of time.
∴ speed is constant
As long as speed is constant the path of an object in uniform motion can have any shape.
Numerical-8
During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? The signal travels at the speed of light that is
3×108ms-1
Solution:-
Speed = Distance / time
∴ Distance = Speed × time
= 3×108ms-1 × 5 min
=3×108ms-1 × 300 sec
=9×1010ms-1
Numerical - 9
A person covers 20m in 5 seconds and then next 20m in 10 seconds along x-axis. Find average speed and average velocity
Solution:- Solve it by using these formula
Average speed = Total distance / total time
Average velocity = Total displacement / total time
Numerical -10
Shyam goes to the market from his home which is 50 m away from the shop in 20 sec. On his way back he visited his friends house which is 10 m away from the shop in 10 sec. Find the average speed and average velocity.
Solution:- Solve it by using these formula
Average speed = Total distance / total time
Average velocity = Total displacement / total time
= Pf – Pi / t
Numerical - 11
John drove south 12 kms at 4km /hr and then east 15 km at 3km/hr. Determine
1- Averrage speed of whole journey
2- Average velocity of whole journey