2026 NASS P2 Q10

A clinic uses an e-bike courier to deliver temperature-sensitive medicine to a care centre 12 km away.

The courier travels against a steady headwind. When riding at a speed of \(v\) km/h relative to the air, where \(v>5\), the actual ground speed is \(v-5\) km/h.

The total energy used for the journey, \(E\) watt-hours (Wh) consists of two parts.

• Motor energy: \(\dfrac{v^2}{80}\) Wh for every kilometre travelled
• Cooling box energy: 112.5 Wh for every hour of the journey

1. Show that \(E=\dfrac{3v^2}{20}+\dfrac{1350}{v-5}\).[3]
2. Find the value of \(v\) for which \(E\) is stationary.[4]
3. Determine whether this stationary value of \(E\) is a minimum.[3]
4. For safety reasons, the courier is only allowed to choose a speed in the range \(12\le v\le18\).
   The battery can supply at most 155 Wh for this journey.
   Determine the speed the courier should choose, and whether the battery limit is satisfied. Justify your answer.[2]