Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
The diagram plots the velocity-time graphs of two particles, $P$ and $Q$, moving along the same straight line. $P$'s graph is made up of four straight-line sections, whereas $Q$'s graph has three straight-line sections. Both particles begin at the same starting point $O$ on the line. $Q$ sets off $2$ seconds later than $P$, and each particle is at rest again at time $t = T$. The maximum velocity of $Q$ is $V\,\text{m s}^{-1}$.
(i)[1]
Find the displacement from $O$ of $P$ at $t = 10$.
(ii)[2]
Find $P$'s velocity at $t = 12$.
(iii)[3]
Given also that $P$ travels a total distance of $49.5\,\text{m}$ in the $T$ seconds of its motion, find the value of $T$.
(iv)[3]
Given also that the acceleration of $Q$ from $t = 2$ to $t = 6$ is $1.75\,\text{m s}^{-2}$, find the value of $V$ and then determine the distance between the two particles when both are at rest at $t = T$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “So, $\tfrac12(10 + 4)\times 6 = 42$” …