Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
The diagram presents the velocity-time graph of a particle $P$ moving along the straight line $AB$, with $v\,\text{m}\,\text{s}^{-1}$ representing the velocity of $P$ at time $t\,\text{s}$. The graph is made up of five straight-line sections. At $t = 0$, the particle is at rest at a point $X$ on the line segment joining $A$ and $B$, and it then travels towards $A$. It is again at rest at $A$ when $t = 2.5$.
(i)[2]
Given that $XA$ is $4\,\text{m}$, find the greatest speed reached by $P$ in this part of the motion.
(ii)[2]
The distance $AB$ is $48\,\text{m}$. The particle takes $12\,\text{s}$ to go from $A$ to $B$ and is at rest at $B$. For the first $2\,\text{s}$ of this stage $P$ accelerates at $3\,\text{m}\,\text{s}^{-2}$, reaching a speed of $V\,\text{m}\,\text{s}^{-1}$. Find the value of $V$.
(iii)[3]
Find the value of $t$ at which $P$ starts to decelerate during this stage.
(iv)[2]
Find the deceleration of $P$ immediately before it reaches $B$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use area under graph equals distance travelled: $\tfrac12 \times 2.5 \times v_{\max}=4$” …