Two particles P and Q located at the points w | vedclass

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Question

(A) The distance $PQ$ between the two particles is given by the distance formula: $PQ = \sqrt{((t+1) - t)^2 + ((t^3 - 6t - 6) - (t^3 - 16t - 3))^2}$ $

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) The distance $PQ$ between the two particles is given by the distance formula: $PQ = \sqrt{((t+1) - t)^2 + ((t^3 - 6t - 6) - (t^3 - 16t - 3))^2}$ $PQ = \sqrt{(1)^2 + (t^3 - 6t - 6 - t^3 + 16t + 3)^2}$ $PQ = \sqrt{1 + (10t - 3)^2}$ To find the minimum distance, we minimize $PQ^2 = 1 + (10t - 3)^2$. Since $(10t - 3)^2 \geq 0$ for all real $t$, the minimum value of $(10t - 3)^2$ is $0$ when $10t - 3 = 0$, i.e.,$t = 0.3$. Thus, the minimum distance is $\sqrt{1 + 0} = 1$.

Two particles $P$ and $Q$ located at the points with coordinates $P(t, t^3-16t-3)$ and $Q(t+1, t^3-6t-6)$ are moving in a plane. The minimum distance between them in their motion is

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