Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle $A$, travelling along a straight horizontal track at a constant speed of $8\text{ m s}^{-1}$, goes past a fixed point $O$. Four seconds later, a second particle $B$ goes past $O$, moving along a parallel track in the same direction as $A$. Particle $B$ is moving at speed $20\text{ m s}^{-1}$ as it passes $O$ and has a constant deceleration of $2\text{ m s}^{-2}$. $B$ comes to rest when it returns to $O$.
(a)[3]
Find expressions, in terms of $t$, for the displacement from $O$ of each particle $t$ seconds after $B$ passes $O$.
(b)[3]
Find the values of $t$ when the particles are the same distance from $O$.
(c)[3]
On the axes provided, sketch the displacement-time graphs of both particles for $t$ values from $0$ to $20$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use suvat to write an expression for $s_A$ or $s_B$.” …