Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
An elevator is drawn upward by a cable. It speeds up vertically at $0.4\,\text{m s}^{-2}$ for $5\,\text{s}$, then continues at a steady speed for $25\,\text{s}$. After that, it slows down at $0.2\,\text{m s}^{-2}$ until it is stationary.
(a)[3]
Find the greatest speed of the elevator and then sketch a velocity-time graph for its motion.
(b)[2]
Find the overall distance covered by the elevator.
(c)[3]
The elevator has mass $1200\,\text{kg}$ and a crate of mass $m\,\text{kg}$ is resting on its floor. If the tension in the cable while the elevator is slowing down is $12\,250\,\text{N}$, find the value of $m$.
(d)[3]
Find the greatest magnitude of the force exerted on the crate by the floor of the elevator, and give its direction.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The greatest speed is $2\ \text{m s}^{-1}$” …