Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
An elevator travels vertically while being held by a cable. The diagram presents a velocity-time graph that represents the elevator’s motion. The graph is made up of $7$ straight line segments. The elevator first accelerates upwards from rest to a speed of $2\,\text{m s}^{-1}$ in $1.5\,\text{s}$, then continues at this speed for $4.5\,\text{s}$, before slowing to rest in $1\,\text{s}$. It then stays at rest for $6\,\text{s}$, before accelerating downwards to a speed of $V\,\text{m s}^{-1}$ over $2\,\text{s}$. The elevator then moves at this speed for $5\,\text{s}$, before slowing to rest in $1.5\,\text{s}$.
(a)[1]
Determine the acceleration of the elevator during the first $1.5\,\text{s}$.
(b)[2]
Since the elevator starts and ends its trip on the ground floor, determine $V$.
(c)[3]
The total mass of the elevator and passengers on the upward trip is $1500\,\text{kg}$. Assuming no resistance to motion, find the tension in the elevator cable on the upward journey when the elevator is decelerating.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Acceleration $=\frac{4}{3}\text{ m s}^{-2}$” …