Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A car with mass $1100\,\text{kg}$ leaves O from rest and travels along the road OAB. OA is a straight stretch of length $1760\,\text{m}$, and it slopes to the horizontal, with A $160\,\text{m}$ above the level of O. AB is a straight horizontal stretch. As the car moves, the driving force is $1800\,\text{N}$ and the resistance to the car’s motion is $700\,\text{N}$. When the car has covered $x\,\text{m}$ from O, its speed is $v\,\text{m s}^{-1}$.
(i)[4]
For the car’s travel from O to A, write the increase in kinetic energy in terms of $v$ and the increase in potential energy in terms of $x$. Hence determine the value of $k$ in $kv^2 = x$ for $0 \le x \le 1760$.
(ii)[4]
Show that $v^2 = 2x - 3200$ when $x \ge 1760$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Increase in KE $= 550v^2$” …