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Positive Sides of Knowing about Negative Signs

positive-negative-signsAs the old adage goes, ďLooks can be deceptive,Ē the same at times holds good in the realm of physics. What appears to be insignificant can have astronomical bearing on the results of some problems. In this post we will be focusing on one such thing, i.e. the negative signs. Many a times, I have seen my students getting perplexed when they encounter a negative sign as a result at the end of some tedious mathematical calculations lurking in some physics problems. They get frustrated assuming that all their effort went in vain when the result is negative.

I have just one word for it. Relax!

There is no need to panic. There can be various implications that can be derived from a negative result bearing the negative sign. So, get ready for some GYAAN on how you can interpret results with negative signs after doing your calculation.

In Physics, Mathematics often generates answers that you might not have thought of as possibilities. If you get more answers than you expect, do not automatically discard the ones that do not seem to fit. Examine them carefully for physical meaning.

For example, if the time is your variable, even a negative value can mean something; negative time simply refers to time before t=0, the (arbitrary) time at which you decided to start your stopwatch.

Here is another misconception; in common language, the sign of acceleration has a nonscientific meaning: positive acceleration means that the speed of an object is increasing, and the negative acceleration means that the speed is decreasing (the object is decelerating). However in many problems of Kinematics, the sign of acceleration indicates a direction, not whether an objectís speed is increasing or decreasing.

For example, if a car with an initial velocity v= -25 m/s is braked to a stop in 5 s, then a(avg) = +5 m/s^2. The acceleration is positive, but the carís speed has decreased. The reason is the difference in signs: the direction of the acceleration is opposite that of the velocity.

 

Problem Solving Tactics in Physics (Motion in One Dimension)

Have you ever experienced this dichotomy: ďI know the concepts, but I find it difficult to solve the problemsĒ? This is not just the case with you. Most of the students are well versed with the theoretical concepts in physics, but they falter, when it comes to problem solving.† Relax! Not a big issue. You are at the right place and since you are reading this post, I am sure that you are a motivated kid and want to improve. This is enough to do the trouble-shooting.

In this entry, we will try to understand the common hurdles that are detrimental to your score, while solving complex Physics problems. For this entry, we will just concentrate on the topic Motion in One Dimension.

Tactic 1: Do You Understand the Problem?

For beginning problem solvers, no difficulty is more common than simply not understanding the problem. The best test of understanding is this: Can you explain the problem in your own words?

Letís try out one problem:

You drive a pick-up truck along a straight road for 8.4 km at 70 km/h, at which point the truck runs out of gasoline and stops. Over the next 30 min, you walk another 2.0 km farther along the road to a gasoline station.

What is your overall displacement from the beginning of your drive to your arrival at the station?

What is the time interval ?t from the beginning of your drive to your arrival at the station?

What is your average velocity Vavg from the beginning of your drive to your arrival at the station?

Find it both numerically and graphically.

In the above problem, the given data allow you to find your net displacement ?x in part (a) and the corresponding time interval ?t in part (b). Also, in part (c) the unknown is your average velocity Vavg. So, itís important to identify the unknown and to find the connection between the unknown and the known data.

Here, the connection is Vavg =†† ?x /?t

Tactic 2: Are the Units OK?

Be sure to use a consistent set of units when putting numbers into the equations. In the above problem, the logical units in terms of the given data are kilometers for distance, hours for time intervals, and kilometers per hour for velocities, you may sometimes need to make conversions.

Tactic 3: Is Your Answer Reasonable?

Does your answer make sense? Is it far too large or far too small?

Is the sign correct? Are the units appropriate? If the answer is no, go back and check.

For example in part (C) of above problem, the correct answer is 17km/hr. if you find 0.00017 km/h, -17 km/h, 17 km/s, or 17,000 km/h, you should realize at once that you have done something wrong. The error may lie in your method, in your algebra, or in your number calculation.

Keep visiting TCYonline.com for more tips and tricks on exam prep.

Remember, we at TCY are committed to your success.

 

Translating Verbal Expressions into Algebraic Expressions

Translating verbal expressionsIf you are preparing for†any competitive exam, you cannot afford to condone the importance of Algebra. The Maths component of any test heavily relies on Algebra and one of the trickiest areas in Algebra is the translation of English expressions into algebraic expressions or statements.

Many problems on your test will be word problems. Being able to translate word problems from English into mathematical expressions or equations will help you to score high on the test. The following table translates some commonly used words into their mathematical equivalents:

Translation Table
Words Math way to say it
Is, as, was, has, cost = (equals)
Of X(times)
Percent /100 (the percent number over 100)
X percent x/100
X and Y X + Y
The sum of X and Y X + Y
The difference between X and Y X - Y
X more than Y X + Y
X less than Y Y Ė X
The product of X and Y XY
The square of X X^2
X is greater than Y X > Y or Y<X
 

Tips & Tricks to Solve Data Sufficiency Problems : Can I or Canít I?

Hello and Welcome back,

Data Sufficiency

This is the typical dilemma posed by most. You donít need to solve the question, but you have to simply decide if the given information or data in the two statements is enough to answer the question posed. Thatís it? Sounds simple right! It may not be that simple though. You need to have a firm grasp on various fundamentals related to logic or Maths, which may help you to breeze through tricky Data Sufficiency questions. On the other hand if your fundamentals arenít that sharp, then better pull up your socks or it is going to be tedious toil.

In this post, we will try to enlighten you about the various DS question types and the approach needed to crack them. We hope this is going to be an interesting and useful read.

Are you ready?

So, Letís Go!

The format of a data sufficiency problem is as follows:

  1. Basic Data: The question has limited available data and could include geometrical figures, graphs and algebraic statements. Examples:
    1. How old is Ravi?
    2. Is x^2 > x?
    3. What is the area of the triangle ABC?
    As a rule, the basic data is insufficient to arrive at a solution.
  2. Two Statements: To see whether we can arrive at a solution or not, there are two separate statements succeeding the given question containing additional data, which may be an aid to arrive at a possible solution. Normally, the alternatives given are as follows:
    1. :† Statement (I) alone is sufficient but statement (II) alone is not sufficient to answer the question asked.†††††††††
    2. :† Statement (II) alone is sufficient but statement (I) alone is not sufficient to answer the question asked.
    3. :† Both statements (I) and (II) together are sufficient to answer the question asked but neither of the† statement alone is sufficient to answer the question asked.
    4. :† Each statement is sufficient by itself to answer the question (THOUGH THE ANSWER,†† IF COMPUTED, MAY BE DIFFERENT).
    5. :† Statements (I) and (II)

      together

      are

      not

      sufficient to answer the question asked and additional information regarding the question is needed.
 

The BIG Question: How to Crack A Logical Reasoning Question?

Hello and welcome back.

Logic is omnipresent. It is ubiquitous in any competitive exam or be it any standardized test. You just canít escape any test without encountering these fiends i.e. Logical Reasoning Questions. It is nothing but daily commonsense that is tested in academic or professional settings. Nothing more than being street-smart is required to crack these questions. If you are street-smart in the true sense, these questions will just be a cake walk for you or else always follow use TCY ís 5-step approach.

TCYís 5-Step Approach:

  1. Read the Question first to see what to look for in the ARGUMENT vis-ŗ-vis assumption, inference, strengthen/weaken, etc.
  2. Read the ARGUMENT with that point of view.
  3. Translate in your own wordsÖ. in English, Hindi or your own language to find out what point/conclusion the author is trying to make.
  4. Pre-phrase your answer, i.e. predict the answer before you look at the answer choices. Though this is not that simple and sometimes you are not able to find out one, but this will definitely enhance your thinking and you will have a better understanding of the given argument.
  5. Choose the answer. While doing so, use the PoE (Power of Elimination). It will be very helpful through all sections of the EXAM.††††††††† †††††††††††

Assumption Questions:

There are mainly three parts of an ARGUMENT:

Conclusion: †What point is the author trying to make or the claim of the argument.

Evidence:††† What evidence (if any) is there for the support of the conclusion?

Assumption:† What assumption is required to reach the conclusion of the argument?

Assumption

bridges

the gap between the conclusion and the evidence. It means that if the assumption is not true, the conclusion cannot be reached.

Note:

Assumption is the bridge between the conclusion and the evidence.

Evidence-conclusion

You cannot reach the conclusion if the bridge is broken

Keywords for Conclusion and Evidence:

Conclusion Words Evidence Words
therefore because
thus for
so since
as a result of due to
hence as
it follows
it leads to

Here's an example:

All men are intelligent. Therefore, Harish is intelligent.

Now,

Therefore, Harish is intelligent --------- conclusion

All men are intelligent --------- evidence

What is the assumption in the argument above if BOTH the given statements are true?

Simple, Harish is a man.

The above argument may not have been true, if Harish had not been a man. Thus, this assumption has to be true for the conclusion to be reached.

So keep visiting TCYonline.com for more tips and tricks for exam preparation.

Remember, we at TCY are committed to your success.

 
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