Two particles $P$ and $Q$ lie on the same straight line. At time $t=0$, $P$ is at $A$ and

Question

Two particles $P$ and $Q$ lie on the same straight line. At time $t=0$, $P$ is at $A$ and $Q$ is at $B$, where $AB=24$ metres. They move towards each other. The velocity of $P$ towards $B$ is $3\sqrt{t}\text{ m s}^{-1}$, while the velocity of $Q$ towards $A$ is $t\text{ m s}^{-1}$. (i) Taking distance from $A$ towards $B$ as positive, find the positions of $P$ and $Q$ at time $t$. (ii) Show that the particles meet when $t=4$. (iii) Find the distance of the meeting point from $A$.

Accepted Answer

(i) $x_P=2t^{3/2}$, $x_Q=24-\dfrac12t^2$; (ii) $t=4\text{ s}$; (iii) $16\text{ m from }A$

Opposing power-law motions

Opposing power-law motions

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