SPEED, TIME AND DISTANCE capsule

Did you ever wonder how fast you run?
I never did!
But , seriously the way the speeds and distances work , can play a much vital role in daily life,
suppose you depart from a station and you know the speed of the bus you are in and want to calculate if with the present speed , will you be able to get to your destination in time....
So, lets see some of these concepts,


RELATION BETWEEN SPEED, TIME AND DISTANCE:

SPEED = DISTANCE / TIME 

, Where speed can have any measuring unit like it could be in metre per sec ,or, metre per hour ,or, kilometre per hour , or any thing , and same applies to time and distance too , there units also can have different measuring units .

so first of all lets see what is a unit ,
so unit is the way how you measure a quantity like and all the units have some reference associated to each other , below is the reference chart of units ,

INTERNATIONAL SYSTEM OF UNITS
International System Of Units
SI UNIT CONVERSION FACTOR
SI UNIT CONVERSION FACTOR

DISTANCE:
This is the length of the path that has been travelled by any object or a person between any two sites . The unit of distance is m or km.

SPEED:
The distance travelled by any object or a person in some unit time . It's unit is m/s or km/h .

Here , are a bunch of formulas coming ,
Tip : note down the formulas atleast 3 times

SOME FORMULAE:

  • SPEED = DISTANCE / TIME
  • AVERAGE SPEED = TOTAL DISTANCE TRAVELLED / TOTAL TIME TAKEN 
  • If A travels having a speed of x km/h for t1 h and with speed y km/h for next t2 h , then             AVERAGE SPEED = ( x*t1 + y*t2) / (t1+t2) 
  • If you want to convert the from m/s to km/h or from km/h to m/s,                                                        m/s -> km/h    (multiply the speed by 5/18)    ,     km/h ->  m/s     (multiply the speed with 18/5)
  • When a man / vehicle / object covers two equal distances with the speed of x km/h and y km/h , then the average speed of the man/ object for the whole journey will be ,                                         (2*x*y) / (x+y)
  • When an object changes its speed with in the ratio of a:b, then the ratio of time taken becomes b:a
  • If two objects are moving in the same direction with speeds x and y km/h(where , x>y) starting from the same point and going into the same direction , then their relative speed  will be (x-y) km/h. Whereas if they move in different directions , then their relative speed will be (x+y)
  • If an object changes its speed to (x/y) of its normal speed , but gets late by t min, then the normal time taken by it , = (t*x) / (y-x),    whereas if that object changes its speed to (x/y) of its normal speed and reaches early by t min , then normal time taken by him, = (t*x) / (x-y)
  • If an object travels from A to B with a speed of x km/h and reached t1 ,time after some fixed time  and when it propagates with a speed of y km/h from A to B , it reaches its destination t2 time before fixed time , then the distance between A and B = X*Y*(t1+t2) / (Y-X) 
  • If any object travels form A to B with a speed of x km/h and reaches t1 time late. Later it has increased its speed by y km/h to cover the same distance , then it will still get late by t2 time , then the distance between A and B will be ,                                                                                   = (T1-T2)*(X+Y)*X/Y  
  • Suppose their are two objects that start at the same time from points A and B towards each other and after crossing each other , they will take t1 and t2 time in getting to the points B and A , respectively . Then ,      Speed of A: Speed of B = √t2 : √t1
  • Suppose the ratio of the speeds of A and B is x:y , then the ratio of time taken by them to cover the same direction is ,   1/X : 1/Y i.e. Y:X 
  • The distance covered by a train in passing a pole , or a standing man , or a single post ,or any object (of some negligible length ) is equal to the length of the train.
  • If a train of length l1 m passes through a bridge , a platform of length l2 m, the running train travels a distance (l1 + l2) m.
  • If a train having a length of l1 m , and speed v1 m/s. Another train of length l2 m and speed v2 m/s are running on two parallel tracks in the same direction , then the faster train will over take slower in (l1 + l2) / (v1 - v2)  s , if (v1 > v2 ) and in (l1 + l2 ) / (v2 - v1) s , if (v2 > v1)
  • If two trains that are of length l1 and l2 km , moving in opposite direction with speeds u km/h and v km/h, respectively , then the time taken to cross each other ,                                               = (l1 + l2) / (u + v)

FORMULAE REGARDING TO BOATS AND STREAM -

->    IF THE SPEED OF A BOAT (OR  A BODY ) IN STILL WATER BE X KM/H AND THAT OF  STREAM BE Y KM/H, THEN    

SPEED OF  BOAT DOWNSTREAM = (X + Y) KM/H
SPEED OF BOAT UPSTREAM         = ( X - Y) KM/H

->    LET THE SPEED OF BOAT IN DOWNSTREAM = U KM/H , SPEED OF UPSTREAM =V KM/H ,THAN 

(A)  SPEED OF BOAT IN STILL WATER =(U + V) / 2 KM/H
(B)  SPEED OF STREAM (CURRENT) = (U - V ) / 2  KM/H

Lets do some exercises now,
SPEED, TIME AND DISTANCE 1
SPEED, TIME AND DISTANCE EXERCISE 1

SPEED, TIME AND DISTANCE 2
SPEED, TIME AND DISTANCE EXERCISE 2

SPEED, TIME AND DISTANCE 3
SPEED, TIME AND DISTANCE EXERCISE 3

SPEED, TIME AND DISTANCE 4
SPEED, TIME AND DISTANCE EXERCISE 4 AND HINTS AND SOLUTIONS 1

SPEED, TIME AND DISTANCE 5
HINTS AND SOLUTIONS 2

SPEED, TIME AND DISTANCE 6
HINTS AND SOLUTIONS 3

SPEED, TIME AND DISTANCE 7
HINTS AND SOLUTIONS 4

SPEED, TIME AND DISTANCE 8
HINTS AND SOLUTIONS 5

SPEED, TIME AND DISTANCE 9
HINTS AND SOLUTIONS 6
thanks for reading this at www.mathcapsule.com

Comments

Post a Comment

Popular posts from this blog

AREA AND PERIMETER OF PLANE FIGURES math capsule

Image
Today we are going to learn about the A rea and Perimeter of Plane Figures . These include various figures like, square , rectangle , quadrilateral , parallelogram , rhombus , trapezium , right angled triangle , isosceles triangle , scalene triangle, equilateral triangle , circle , circular ring , semi circle , quadrant of circle , area of sector , regular polygon , etc. All these are important plane figures and today we are going to study about their area and perimeter and how we can compute them easily . Tip : get a pen and paper and write each formula for five to six times so that you may easily remember the formulae of  area and perimeter of plane figures . So, lets begin ,
Read more

BEST BOOKS FOR MATHEMATICS math capsule

Image
Hi in this blog post i am going to tell you , What are the best books for you to improve your mathematics, There are various people and they have different needs of what they want to read about , actually there needs depend upon may be what they are presently pursuing or what they want others to read. Here is my list of recommended best books for you to improve your mathematics , so that you may learn better . I have divided the whole things into categories so that it may get easier for you to get an idea of what book you want .
Read more

RD Sharma - The Big B Of Maths

Image
R D Sharma is not the quite author you'd come across at lit fests. however his bestselling books have helped several CBSE students lose their dread of maths. Sunday Times profiles the tutor turned web star He dreams of algorithms that might offer the general public nightmares. And, spends each waking hour thinking of how to clarify ideas like 'series answer of linear differential equations'. Meet Dr Ravi Dutt Sharma — math teacher and author of twenty five reference books — whose name evokes the maximum amount awe because the subject he teaches. And tho' students have used his thick tomes for the last thirty one years to ace the terrible maths examination, it's solely recently that a spoof video turned the tutor into a YouTube star.
Read more

HCF AND LCM OF POLYNOMIALS math capsule

Image
I hate long articles or blog posts , don't you ? That's why i write mine really very short, descriptive and covering all the concepts in one go . This post is regarding the hcf and lcm of polynomials and monomials. If you want to learn about the hcf and lcm of numbers then click this yellow link below . It will take you to another article . Sorry ;)   HCF and LCM   HCF OF POLYNOMIALS                                      The highest common factor of two or more algebraic expressions is the factor of the highest degree which divides each of the expressions without a remainder. It is denoted by HCF or GCD. It is a convention to take HCF in such a way that the coefficient of the highest power of the variable is positive.
Read more

SIMPLE INTEREST (SI) AND COMPOUND INTEREST (CI) math capsule

Image
How much is my bank going to pay me for depositing a certain amount of money into my bank account? Has this question came into your mind ? If yes, then you are going to master all ways how you can calculate this in this blog post on SI and CI. SIMPLE INTEREST : When we borrow some money , then customarily the money lender or the person who is giving us the money uses to charge some extra amount of money in lieu of the money that he has lent us.This extra money by the money lender is called Interest.
Read more

LOGARITHM math capsule

Image
log ! log ! log! You know this was the most scary term in mathematics for me when i was in high school! But when i studied it , it became the most easy concept to learn and i used to do the problems in seconds . And sometimes that too without using pen and paper. LOGARITHM If 'a' is a positive real number other than 1 and 'b' is a rational number such that aⁿ= B then we say that logarithm of B to base 'a' is n or 'b' is the logarithm of N to base 'a', written as  logₐ B = n So, aⁿ = B <=> log ₐ B = n e.g. 7º = 1 <=> log ₇ 1 = 0
Read more

Internet Of Things | Explained | Meaning | Real life applications

Image
The "Internet of things" (IoT) is changing into associate progressively growing topic of spoken communication each within the geographic point and out of doors of it. it is a conception that not solely has the potential to impact however we have a tendency to live however conjointly however we have a tendency to work. however what precisely is that the "Internet of things" and what impact is it aiming to wear you, if any? There ar lots of complexities round the "Internet of things" however i would like to stay to the fundamentals. several technical and policy-related conversations ar being had however many folks ar still simply attempting to know the inspiration of what the euphemism these conversations ar concerning. Let's begin with understanding a couple of things. Broadband web is become a lot of wide obtainable, the value of connecting is decreasing, a lot of devices ar being created with Wi-Fi capabilities and sensors engineered into them,
Read more

HOW I GOT ADSENSE APPROVED IN JUST 11 DAYS !

Image
This post is going to be deviating you from the topics of mathematics, but i am including this as because i got a lot of requests of how to do this , HOW CAN ONE APPROVE HIS / HER ADSENSE ACCOUNT IN JUST A FEW DAYS? This question always trouble a lot of persons , when they seek Adsense approval for their new blogs. They usually search on the internet on how to do it in only a few days. And most of the times they are left empty handed. So, in this post i am going to tell you guys how i got my Google Adsense in just 11 days from the very start of my blog . Tips: Do follow what i am going to tell you guys in this blog post , really this will help you in a great way . I am going to tell you the secrets that i did with my blog so that you may too get a Google Adsense account.
Read more

Search Engine Optimisation | meaning | tutorial | techniques | tools | THE COMPLETE GUIDE

Image
I. Introduction – what's SEO Whenever you enter a question in an exceedingly program and hit 'enter' you get an inventory of net results that contain that question term. Users usually tend to go to websites that area unit at the highest of this list as they understand those to be a lot of relevant to the question. If you've got ever questioned why a number of these netsites rank higher than the others then you need to understand that it's as a result of a robust web selling technique referred to as program improvement (SEO). SEO may be a technique that helps search engines notice and rank your website beyond the numerous different sites in response to a probe question. SEO therefore helps you get traffic from search engines. This SEO tutorial covers all the mandatory data you wish to understand concerning program improvement - what's it, however will it work and variations within the ranking criteria of major search engines. 1. However Search Engine
Read more

SURFACE AREA AND VOLUME OF SOLIDS math capsule

Image
In this chapter we will study to find the surface area and volume of solid figure , like parallelepiped , cube, cuboid, cylinder , cone , frustum of cone , sphere and hemisphere and we will study to find the surface area and volume of combination of solid figures combination of two or more different or similar solid figures. SOLID FIGURES The objects which occupy space (i.e. they have three dimensions ) are called solids. The solid figures can be derived from the plane figures. e.g. In figure (i) , we have a paper cut in the form as shown. It is a plane figure. But when we fold the paper along the dotted lines, a box can be made as shown in figure (ii) , which occupies some part of the space. It has more than two dimensions and therefore it fulfils the criteria of being a solid figure.
Read more