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(B) The position of the particle is given by the equation $x = a + bt^2$.To find the instantaneous velocity $v$,we differentiate the position $x$ with

Vedclass · Accepted Answer

$18$

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(B) The position of the particle is given by the equation $x = a + bt^2$.To find the instantaneous velocity $v$,we differentiate the position $x$ with respect to time $t$:$v = \frac{dx}{dt} = \frac{d}{dt}(a + bt^2)$Since $a$ is a constant,its derivative is $0$. Thus,$v = 2bt$.Given $b = 3 \, cm/s^2$ and $t = 3 \, s$,we substitute these values into the velocity equation:$v = 2 	imes 3 	imes 3 = 18 \, cm/s$.Therefore,the instantaneous velocity at $t = 3 \, s$ is $18 \, cm/s$.

The motion of a particle is described by the equation $x = a + bt^2$ where $a = 15 \, cm$ and $b = 3 \, cm/s^2$. Its instantaneous velocity at time $t = 3 \, s$ will be ........ $cm/s$.

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