Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
The diagram depicts a velocity-time graph representing the motion of a cyclist. It is made up of five straight-line sections. Starting from rest, the cyclist speeds up to $5\,\text{m s}^{-1}$ in $10\,\text{s}$, then continues at this constant speed for another $20\,\text{s}$. The cyclist then goes down a hill and accelerates to speed $V\,\text{m s}^{-1}$ over $10\,\text{s}$. That speed is then kept for a further $30\,\text{s}$ before the cyclist slows to rest over $20\,\text{s}$.
(i)[1]
Find the cyclist’s acceleration in the first $10$ seconds.
(ii)[3]
Show that the cyclist’s total distance in the $90$ seconds of motion can be written as $(45V + 150)\,\text{m}$. Hence find $V$, given that the cyclist’s total distance is $465\,\text{m}$.
(iii)[4]
The combined mass of the cyclist and the bicycle is $80\,\text{kg}$. The cyclist experiences a constant resistance to motion of $20\,\text{N}$. Use an energy method to find the vertical distance descended during the downhill section from $t = 30$ to $t = 40$, assuming that the cyclist does no work during this time.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate acceleration: $a = 0.5\,\text{m s}^{-2}$” …