Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle with mass $0.4\,\text{kg}$ is let go from rest from a point $1.8\,\text{m}$ above the water surface in a tank. Its speed does not change instantaneously as it enters the water. While it is in the water, the water exerts an upward force of $5.6\,\text{N}$ on the particle.
(i)[2]
Calculate the velocity of the particle at the moment it reaches the water surface.
(ii)[4]
Calculate the time from the instant the particle enters the water until it is momentarily at rest in the water. You may assume that the tank is deep enough for the particle not to touch the bottom.
(iii)[3]
Sketch a velocity-time graph for the motion of the particle from the instant of release until it becomes momentarily at rest in the water.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Kinetic energy gain = gravitational potential energy lost: $0.4g \times 1.8 = \tfrac{1}{2} \times 0.4 v^2$” …