A particular substance is cooled by a stream of cold air at a constant temperature of

MATHEMATICS · Numerical · CBSE · Mathematics · Differential Equations · Differential Equations

Problem

A particular substance is cooled by a stream of cold air at a constant temperature of 5∘C5^\circ\text{C}. The rate of cooling is directly proportional to the square of the difference between the temperatures of the substance and air. If the substance is cooled from 40∘C40^\circ\text{C} to 30∘C30^\circ\text{C} in 15 min15\text{ min} and its temperature after 1 hour1\text{ hour} is t∘Ct^\circ\text{C}, find [t]2\frac{[t]}{2}, where [⋅][\cdot] represents the greatest integer function.

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