Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

Particles $P$ and $Q$ move along a straight line on a rough horizontal plane, and friction is the only horizontal force acting on the particles.
(i)[2]

Find the deceleration of each particle, given that the coefficient of friction between $P$ and the plane is $0.2$, and between $Q$ and the plane is $0.25$.

(ii)[5]

At a particular instant, $P$ passes through point $A$ and $Q$ passes through point $B$. The distance $AB$ is $5\,\mathrm{m}$. The velocities of $P$ and $Q$ at $A$ and $B$ are $8\,\mathrm{m\,s^{-1}}$ and $3\,\mathrm{m\,s^{-1}}$, respectively, both along the direction $AB$. Find the speeds of $P$ and $Q$ immediately before they collide.

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