Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A car with mass $1230\,\text{kg}$ speeds up from $4\,\text{m s}^{-1}$ to $21\,\text{m s}^{-1}$ over $24.5\,\text{s}$. The table beneath gives matching values of time $t\,\text{s}$ and speed $v\,\text{m s}^{-1}$.
(i)[2]
From the table values, determine the car’s average acceleration for $0 \le t \le 0.5$ and for $16.3 \le t \le 24.5$.
(ii)[5]
As the car’s speed rises, the engine’s power output stays constant at $P\,\text{W}$, while the resistance to the car’s motion remains constant at $R\,\text{N}$. If the answers from part (i) are taken as approximately the accelerations at $v = 5$ and at $v = 20$, find estimates for $P$ and $R$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply average acceleration formula $a = \Delta v / \Delta t$ to each interval.” …