Techniques of Scientific Management
(i) Time Study
Time study is a technique used to determine the standard time required to perform a specific task or job by observing and recording task elements to establish the most efficient method.
(ii) Motion Study
Motion study analyzes worker movements to eliminate unnecessary actions and find the most efficient sequence of motions for task completion.
(iii) Fatigue Study
Fatigue study determines optimal rest intervals to reduce worker exhaustion and maintain productivity levels.
| Technique | Primary Focus |
|---|---|
| Time Study | Optimizing task completion time |
| Motion Study | Minimizing unnecessary movements |
| Fatigue Study | Managing worker rest and wellbeing |

A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).