Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A frictional force of magnitude $0.12\,\text{N}$ acts on a small block of mass $0.15\,\text{kg}$ while it is travelling over a horizontal surface. The block is launched from a point $X$ on the surface with speed $3\,\text{m s}^{-1}$. After $2\,\text{s}$ it reaches a vertical wall at point $Y$ on the surface. It rebounds from the wall and then travels straight back towards $X$ until it stops at point $Z$ (see diagram). When the block strikes the wall, its kinetic energy decreases by $0.072\,\text{J}$. At time $t\,\text{s}$ after leaving $X$, the velocity of the block in the direction from $X$ to $Y$ is $v\,\text{m s}^{-1}$.
(i)[9]
Find the values of $v$ when the block reaches $Y$ and when it leaves $Y$, and also determine the value of $t$ when the block is at rest at $Z$. Sketch the velocity-time graph.
(ii)[4]
The block’s displacement from $X$, measured in the direction from $X$ to $Y$, is $s\,\text{m}$ at time $t\,\text{s}$. Sketch the displacement-time graph. Mark on your graph the values of $s$ and $t$ when the block is at $Y$ and when it comes to rest at $Z$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applying Newton’s second law gives $-0.12 = 0.15a$” …