(C) The equation of motion is given by $s = ut - 6.3t^2$.To find the velocity $v$,we differentiate $s$ with respect to $t$:$v = \frac{ds}{dt} = \frac{

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(C) The equation of motion is given by $s = ut - 6.3t^2$.To find the velocity $v$,we differentiate $s$ with respect to $t$:$v = \frac{ds}{dt} = \frac{d}{dt}(ut - 6.3t^2) = u - 12.6t$.At the maximum height,the velocity of the stone is zero:$v = 0$.Given that the stone reaches its maximum height at $t = 3$ $sec$,we substitute these values into the velocity equation:$0 = u - 12.6(3)$.$0 = u - 37.8$.$u = 37.8$ $cm/sec$.

Class 12 Mathematics Applications of Derivatives Maxima and Minima

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The equation of motion of a stone,thrown vertically upwards is $s = ut - 6.3t^2$,where the units of $s$ and $t$ are $cm$ and $sec$. If the stone reaches its maximum height in $3$ $sec$,then $u =$ ......... $cm/sec$.

A
$18.9$
B
$12.6$
C
$37.8$
D
None of these

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Applications of Derivatives

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Maxima and Minima

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The equation of motion of a stone,thrown vertically upwards is $s = ut - 6.3t^2$,where the units of $s$ and $t$ are $cm$ and $sec$. If the stone reaches its maximum height in $3$ $sec$,then $u =$ ......... $cm/sec$.

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