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Read the passage and answer the questions.
Seema enjoys a roller coaster ride in Ferrari world by first going downwards and then upwards to…
Seema enjoys a roller coaster ride in Ferrari world by first going downwards and then upwards to the maximum height. The relation between the distance travelled (cm) with respect to the time taken to complete the side by Seema is given by the following equation:
$y = 4x - \frac{1}{2}x^2$
where $x = \text{time in seconds}$.
(a)[1.0]
What is the rate of change of displacement with respect to the time?
(b)[1.0]
How many seconds it will take her to go to its maximum height?
Answer
Answer (a)
Official answer key$\frac{dy}{dx} = 4 - \frac{1}{2} \times 2x = 4 - x$.
Final answer: $4 - x$
Answer (b)
Official answer keyTo reach maximum height $\frac{dy}{dx} = 0$
$\therefore 4 - x = 0$
$\therefore x = 4$ sec
and $\frac{d^2y}{dx^2} = -1 < 0$
$\therefore$ Height is maximum after 4 seconds.
Final answer: 4 s
From ISC 2025 Practice Mathematics, question 75.