Future Study Point

# Average Speed and Average Velocity

Average speed and average velocity-The The speed is defined as the distance per unit time and average speed is defined as total distance covered in per unit of total time or the average rate of covering the total distance. The relationship between total distance, time and average speed is, the total distance is the product of total time taken and average speed. The average speed is the total distance covered per unit time and the average velocity is total displacement covered in per unit time is known as average velocity. The average velocity and average speed both are very important in Dynamics or Kinematics in the calculation of net energy. Before we study in detail what is average speed and average velocity, we are needed to study first what are distance and displacement.

Click for online shopping

Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc

Distance. The total distance covered by an object during its journey is known as distance. The distance is a scalar quantity since it is represented by a magnitude only. The S.I unit of distance is meter.

### You can also study related topics

Three Laws of Motion: Class 9 CBSE

Archemed Principal

How to evaluate recoil velocity of gun

If energy is conserved then why do we need to save it for future generations?

What is second law of of motion ?

What is universal law of gravitational force

NCERT Solutions Class 10 Science from chapter 1 to 16

Displacement. The shortest distance between the initial and final position of an object during its journey is known as displacement. Displacement is the vector quantity since it represented by direction and magnitude. The S.I unit of displacement is meter.

### Laptops on very small EMI

Example. Mohan went 12 km west from his house and then turned 5 km towards the north, show the displacement and the distance covered by him.

The distance covered covered by Mohan is = 12 + 5 =17 km

The displacement is = shortest distance = AC

Triangle ΔABC  is the right triangle in which ∠B is the right angle

$\therefore AC=\sqrt{AB^{2}+BC^{2}}=\sqrt{12^{2}+5^{2}}=\sqrt{169}=13$

The displacement covered by Mohan = 13 km

When anything changes its position with respect to time then we say that the thing is in motion. According to the state of motions, it is of two kinds (i) Uniform Motion (ii) Non-Uniform Motion.

(i) Uniform Motion

• A moving car on a busy road.
• A Boy running in the field

(ii) Non-Uniform Motion.

• Moving fan
• Moon around the earth

Distance. The distance is the total distance covered by an object during its travel in a given time.

Displacement. The shortest distance covered by an object during the travel, in other words, the minimum distance from the initial point and final point during the journey of an object.

Average Speed. Per unit of the total distance covered in per unit of the total time is known as average speed.

$Average\: Speed\: = \frac{Total\: distance \: covered}{Total\: time \: taken}$

Average Velocity. Per unit of the total displacement covered in per unit, time is known as average velocity.

$Average \: velocity=\frac{Total \: displacement}{Total\: time}$

Example. Rohit traveled a distance of 24 km through a bicycle in 1 hour and then turned right and traveled 7 km in 10 minutes, find the average velocity and average speed of the bicycle he is cycling.

Solution.

The total distance covered is = 24 + 7 = 31 km

Total time taken = 1 hour + 10 minutes

$1Hr+\frac{10}{60}Hr=\frac{7}{6}Hr$

$Average \: speed=\frac{Total \: distance}{Total\: time}=\frac{31}{7/6}=\frac{186}{7}=26.57$

Therefore average speed is = 26.57 km/h

Total displacement = shortest distance in journey = BC

$BC=\sqrt{AB^{2}+AC^{2}}=\sqrt{24^{2}+7^{2}}=\sqrt{625}=25$

Total displacement = 25 km

Total time is taken = 7/6 Hr

$Average \: velocity=\frac{Total \: displacement}{Total\: time}$

$Average\: velocity=\frac{25}{7/6}=\frac{150}{7}\approx 21.43$

Hence the average velocity of the bicycle is 21.43 km/h

Science and Maths NCERT solution for Class 9 to 12 class

Example. Ramaswami Lingham went to his school with an average velocity of 6 km/h and returned to his home at an average speed of 8 km/h, find his average speed in his journey?

Solution. Let the distance from his home to school is = x km

His speed from home to school = 6 km/h

Time is taken by him from home to school = x/6

Distance from school to home = x km

His speed from school to home = 8 km/h

Time is taken by him from school to home = x/8

Total time taken in total journey = x/6 + x/8 = 7x/24

∴ The total distance he covered = x + x = 2x km

$Average \: speed = \frac{Total \: distance}{Total \: time}=\frac{2x}{7x/24}\approx 6.86$

Therefore the average speed of Ramswami Lingam is 6.86 km/h.

Example. Shyam makes a round of a circular ground in 5 minutes if the radius of the ground is 350 m, find how much distance, displacement,  he will cover in 12.5  minutes?

Solution. Distance covered by Shyam in one round of the ground = circumference of the ground = 2πr

Where r is the radius of the ground which is given to us = 350 m

Distance covered in one round = 2 × (22/7) × 350 = 2200 m

Time is taken to cover one round = 5 minutes

$Speed=\frac{Distance}{Time}$

$=\frac{2200}{5}=440\: meter/min$

Speed = 440 meter/min

Time is given = 12.5 min.

Distance = Speed × Time = 440 × 12.5 = 5500 meter = 5.5 km

In 5 minutes Shyam covers → 1 round

In 1 minute he will cover → 1/5 round

In 12.5 minutes he will cover → 12.5 × 1/5 = 2.5 round

Suppose Shyam starts to move from A then after 2.5 round his position will be at B

The displacement = AB = Diameter of the ground = 400 meter

## Important Science Notes for Class 9 and 10 grade

### Class 10 CBSE Science Notes

Human  reproductive systems of Male & Family

Modes of reproduction used by single organisms-Asexual reproductions

Types of plant tissues

The structure and anatomy of the Heart

Anatomy of the Human brain-Class 10 CBSE

NEET Sylabus and its preparation

Myopia, Hypermetropia and Presbyopia

Human eye structure and its function

Electrical resistance and conductance

Electric Current and Heating effect of Electric Current

What is a potential difference across an electric field ?

Why do the star twinkle but planets don’t

Light reflection, refraction, scattering, and dispersion

What is God particle ?

Class 10 chemistry Viva Voce Questions and Answers

Class 10 Physics Viva Voce Questions and Answers

Class 10 Chemistry Practical Based Questions and Answers

What are the physical and chemical properties of metals?

Type of Chemical Reactions with Complete detail

Chemical properties of Acids and Bases-A note for grade 10 students

What is pH value and its importance in everyday life.

Difference between soaps and detergents

Extraction of metals as per the activity series

Ionic and covalent compounds and the difference between them

### Class 9 CBSE Science Notes

Three Laws of Motion: Class 9 CBSE

Evoporation,Vapourization and Latent heat -Class 9 CBSE notes

What is an atom,molecule and atomicity of a substance?

How to determine Valency,net charge of an ion and Molecular formula of a substance.

Thrust and Pressure : Difference

The Complete Detail of Archimedes Principal

Average Speed and Average Velocity: Differences

How to evaluate recoil velocity of gun

If energy is conserved then why do we need to save it for future generations?

Molar mass,molecular mass and mole concept

What is second law of of motion ?

What is universal law of gravitational force

## NCERT Solutions of Science and Maths for Class 9,10,11 and 12

### NCERT Solutions for class 9 science

CBSE Class 9-Question paper of science 2020 with solutions

CBSE Class 9-Sample paper of science

CBSE Class 9-Unsolved question paper of science 2019

### NCERT Solutions for class 10 maths

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

### Solutions of Class 10 Science Sample Paper and Question Papers for Term-1 and Term 2 2021-22 CBSE Board

Solution of Class 10 Science Question Paper Preboard 2021-22:Term 2 CBSE Board Exam

Solutions of Class 10 Science Sample Paper Term-1 2021-22 CBSE Board

Class 10 Science Sample Paper for Term 2 CBSE Board Exam 2021-22 with Solution

Solutions of Class 10 Science Question Paper Preboard Examination (First) 2021 -22 Class 10 Science

CBSE Class 10 – Question paper of science 2020 with solutions

CBSE class 10 -Sample paper of Science 2020

### NCERT Solutions for class 11 maths

 Chapter 1-Sets Chapter 9-Sequences and Series Chapter 2- Relations and functions Chapter 10- Straight Lines Chapter 3- Trigonometry Chapter 11-Conic Sections Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry Chapter 5-Complex numbers Chapter 13- Limits and Derivatives Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning Chapter 7- Permutations and Combinations Chapter 15- Statistics Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

### NCERT solutions for class 12 maths

 Chapter 1-Relations and Functions Chapter 9-Differential Equations Chapter 2-Inverse Trigonometric Functions Chapter 10-Vector Algebra Chapter 3-Matrices Chapter 11 – Three Dimensional Geometry Chapter 4-Determinants Chapter 12-Linear Programming Chapter 5- Continuity and Differentiability Chapter 13-Probability Chapter 6- Application of Derivation CBSE Class 12- Question paper of maths 2021 with solutions Chapter 7- Integrals Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution