Particle $P$ passes a fixed point $O$ at time $t=0$. Its velocity at time $t$ seconds is \(2

Question

Particle $P$ passes a fixed point $O$ at time $t=0$. Its velocity at time $t$ seconds is $2t\text{ m s}^{-1}$. Two seconds later, particle $Q$ passes $O$ in the same direction with constant velocity $12\text{ m s}^{-1}$. Let $T$ seconds be the time elapsed after $Q$ passes $O$. Express the displacements of $P$ and $Q$ from $O$ in terms of $T$.[2] Find the two values of $T$ at which the particles meet.[3] State which particle overtakes the other at each meeting.[2]

Accepted Answer

(i) $x_P=(T+2)^2$, $x_Q=12T$; (ii) $T=4\pm2\sqrt3\text{ s}$; (iii) $Q$ overtakes $P$ first, then $P$ overtakes $Q$

Delayed-start overtaking twice

Delayed-start overtaking twice

Solution:

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