Particles $P$ and $Q$ move in the same direction along a straight line. At time $t=0$, $P$ i

Question

Particles $P$ and $Q$ move in the same direction along a straight line. At time $t=0$, $P$ is at $O$ and $Q$ is $54$ metres ahead. Their velocities are $6\sqrt{t}\text{ m s}^{-1}$ and $3\sqrt{t}\text{ m s}^{-1}$, respectively. (i) Find the positions of $P$ and $Q$, measured from $O$, at time $t$. (ii) Hence determine the time at which $P$ catches $Q$. (iii) Find the distance travelled by $P$ by the catch time.

Accepted Answer

(i) $x_P=4t^{3/2}$, $x_Q=54+2t^{3/2}$; (ii) $t=9\text{ s}$; (iii) $108\text{ m}$

Same-direction power-law catch-up

Same-direction power-law catch-up

Solution:

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