# Problem Solving Tactics in Physics (Motion in One Dimension)

Have you ever experienced this dichotomy: “I know the concepts, but I find it difficult to solve the problems”? 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?

**Let’s 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, it’s 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.**

# MATRICES ICSE

Matrices is an interesting topic in the field of Mathematics. A matrix is a rectangular arrangement of numbers , as horizontal rows and vertical columns , similar to the arrangement of elements in the Periodic Table . So each number of the matrix can be called as an element of the Matrix. If the number of Rows in a matrix ( A ) is m and the number of Columns is n , then the said Matrix is of the Order m X n and is written as A = (aij) There are different types of Matrices , like 1) Equal Matrix : Two matrices are called as Equal matrices only if they are of the same order and their corresponding elements are equal. 2) Row Matrix : Has only one Row of elements. 3) Column Matrix : Has only one Column of Elements. 4) Square Matrix : The number of Rows and Columns are equal. 5) Zero or Null Matrix : Each element is Zero. 6) Diagonal matrix : All elements except the elements in the main Diagonal are Zero. 7) Unit matrix : Each of its diagonal element is 1 and each of all other or Elements is zero. (Identity Matrix) Addition and Subtraction of matrices : Two matrices of the same order are added by adding their corresponding elements. The element in the 1st row and 1st column of the first matrix is to be added with the element in the first row and first column of the second matrix and placed in the 1st row and 1st column of the newly formed matrix.. Similarly , the other elements of the first Matrix are added to thier corresponding elements in the second matrix . For example A and B are two matrices of the same order , then A+B=B+A But A-B is not equal to B-A This is an important fact the student has to remember while working sums on Matrices. Multiplication of Matrices : The product AB of two matrices A and B is possible only when the number of columns in A is equal to the number of rows in B . A is called the pre-multplier and B is called the post multiplier. The student can follow the following steps while finding the product of two matrices A and B. 1) First multiply the elements of the 1st row of A by the corresponding elements of the 1st column of B and add. The number got after adding becomes the 1st element in the 1st row of the resulting matrix. AB 2)Multiply the elements of the 1st row of A by the corresponding elements of the 2nd column of B and add. This becomes the second element in the first row of the resulting matrix AB. 3)In the same manner , the remaining elements of the first row of the resulting matrix AB can be obtained. 4) Proceeding in the same way , the student can get the elements of the remaining rows of the resulting matrix. AB . Transpose of a Matrix is another interesting fact about a matrix. The transpose of a matrix A is A^T .The elements in A^T can be obtained by interchanging the rows and columns of the given matrix. For example A = 1 2 5 9 then A^T = 1 5 2 9 Important fact about multiplication of Matrices : If the order of matrix A is m X n and the order of matrix B is n X p then the product AB is possible and the order of the product matrix obtained is m X p , i.e number of rows of matrix A X number of columns of matrix B .