Mathematics 9709 · AS & A Level · Forces and equilibrium
Forces and equilibrium — practice question
A particle with mass $3\,\text{kg}$ is released from rest from a point $5\,\text{m}$ above the top surface of a liquid in a container. Its speed does not change instantaneously as it crosses into the liquid. The liquid in the container has a depth of $4\,\text{m}$. While the particle is travelling through the liquid, its downward acceleration is $5.5\,\text{m s}^{-2}$.
(i)[2]
Find the resistance opposing the particle’s motion while it is in the liquid.
(ii)[7]
Sketch the velocity-time graph for the particle’s motion from the instant it starts moving until the instant it reaches the bottom of the container. On your sketch, show the velocity and time when the particle enters the liquid, and also the velocity and time when the particle reaches the bottom of the container.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applying Newton’s second law in the vertical direction gives $3g - R = 3 \times 5.5$” …