The displacement x (in m) of a particle of ma | vedclass

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(A) The displacement $x$ is given as a function of time $t$ by the equation: $t = \sqrt{x} + 3$.Rearranging for $\sqrt{x}$,we get: $\sqrt{x} = t - 3$.

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(A) The displacement $x$ is given as a function of time $t$ by the equation: $t = \sqrt{x} + 3$.Rearranging for $\sqrt{x}$,we get: $\sqrt{x} = t - 3$.Squaring both sides,we obtain the expression for displacement: $x = (t - 3)^2 = t^2 - 6t + 9$.The velocity $v$ of the particle is the derivative of displacement with respect to time: $v = \frac{dx}{dt} = \frac{d}{dt}(t^2 - 6t + 9) = 2t - 6$.To find the displacement when velocity is zero,we set $v = 0$:$2t - 6 = 0 \Rightarrow 2t = 6 \Rightarrow t = 3 \ s$.Now,substitute $t = 3 \ s$ into the displacement equation:$x = (3 - 3)^2 = 0^2 = 0 \ m$.Thus,the displacement of the particle when its velocity is zero is $0 \ m$.

The displacement $x$ (in $m$) of a particle of mass $m$ (in $kg$) moving in one dimension under the action of a force,is related to time $t$ (in $s$) by $t = \sqrt{x} + 3$. The displacement of the particle when its velocity is zero,will be

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