Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line

Kinematics of motion in a straight line — practice question

For a particle travelling along a straight line, its velocity is $v\,\text{m s}^{-1}$ at $t$ seconds after it leaves the fixed point $O$. The diagram displays a velocity-time graph that represents the particle's motion for $t=0$ to $t=16$. It is made up of five straight line sections. The acceleration from $t=0$ to $t=3$ is $3\,\text{m s}^{-2}$. At $t=5$, the particle's velocity is $7\,\text{m s}^{-1}$ and it is momentarily at rest at $t=8$. It then is at rest again at $t=16$. The smallest velocity reached is $V\,\text{m s}^{-1}$.
(i)[3]

Find the distance covered by the particle during the first $8\,\text{s}$ of its motion.

(ii)[4]

Since the particle is at rest again at $t=16$ and its displacement from $O$ is $32\,\text{m}$, find the value of $V$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: At $t=3$, $v = 3 \times 3 = 9$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI