# H. C. Verma Solutions – Chapter 3, Question 12

H. C. Verma, Chapter 3, Question number 12 A particle starts from a point A and travels
along the solid curve as shown below. Find approximately the position B of the particle
such that the average velocity between the positions A and B has the same direction as
instantaneous velocity at B. If we assume the B to be at the point shown
by red dot then the net displacement from A to be is along line AB. Since displacement
is along this line, the direction of the average velocity is also along this line. So, the
direction of average velocity between two points on a curve is same as the direction
of chord joining these two points. Also, at B, the direction of instantaneous
velocity is along the tangent to the path at B. To summarize, the direction of average
velocity is along the chord joining A to B and direction of instantaneous velocity is
along the tangent at point B. If direction of both has to be same, then
the direction of chord joining AB must be same the direction of tangent along B. So,
if we draw a line from A such that it is tangent to the curve then the point of contact of
the line with the curve is B. As us can see, in this case the chord and
tangent, both are same and therefore, the direction of average and instantaneous velocity
is same. The coordinate of this point is approximately
3 meter comma 5 meter. This is our answer. In order to request solution to any question
from H. C. verma book, post the question number and chapter number in comments below. Like
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## 7 thoughts on “H. C. Verma Solutions – Chapter 3, Question 12”

1. Dhrub Raj says:

sir chapter 3 question no.,20, 27, 29, 30 . yeh sb k video hai pr ache se smj nhii aaya hai kia aap kuch help kr skte hai ise video ko improve kr k.. pls reply me fast ..thnk u sir ./

2. SANTOSH VASTRALAYA says:

Can a mathematical solution of this question

3. Aryan Bachhav says:

Sir how you can say 3rd point is b they are opposite in direction

4. Om Printing Press says:

More important than hcv solution

5. Yash Sisodia says:

I want the solution of HCV chapter 3 question number 50

6. Jatish Gupta says:

sir ans of this ques can be (1.5,3) ???
because in that case both have same direction of velocity

7. Kuldeep Borah says: