Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Particles $A$ and $B$ have masses $0.12\,\text{kg}$ and $0.38\,\text{kg}$ respectively. They are connected by the ends of a light inextensible string, which goes over a fixed smooth pulley. $A$ is kept stationary with the string taut, and both sections of the string are vertical. Each particle is $0.65\,\text{m}$ above the horizontal ground (see diagram). $A$ is then released, and $B$ moves downwards.
(i)[2]
Determine the acceleration of $B$ while it is moving downwards.
(ii)[3]
Determine the speed at which $B$ hits the ground and the time it takes to get there.
(iii)[3]
While $B$ stays on the ground, $A$ keeps moving with the string slack and does not reach the pulley. The slack persists until $A$ is again at a height of $1.3\,\text{m}$ above the ground. At that instant, $A$ has been moving for a total time of $T\,\text{s}$. Find $T$ and sketch the velocity-time graph for $A$ over the first $T\,\text{s}$ of its motion.
(iv)[2]
Determine the total distance covered by $A$ in the first $T\,\text{s}$ of its motion.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply Newton’s second law to both masses, or use $a = \frac{M-m}{M+m}g$.” …