Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A cyclist and her bicycle together have a combined mass of $60\text{ kg}$. She moves along a horizontal straight line, while a constant force of $150\text{ N}$ acts in the direction of travel. The motion is resisted by a force with magnitude $12v\text{ N}$, where $v\text{ m s}^{-1}$ is the cyclist’s speed at time $t\text{ s}$ after she goes past a fixed point $A$.
(i)[2]
Show that the relation $5\frac{dv}{dt} = 12.5 - v$ is satisfied.
(ii)[4]
Since the cyclist passes through $A$ with speed $11.5\text{ m s}^{-1}$, solve this differential equation to establish that $v = 12.5 - e^{-0.2t}$.
(iii)[3]
Find the cyclist’s displacement from $A$ as a function of $t$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Newton’s second law: $60\,dv/dt = 150 - 12v$” …