| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2018 |
| Session | June |
| Topic | Work done and energy |
| Type | Resistance as kv² - finding constant k |
| Difficulty | Moderate -0.3 This is a straightforward two-part mechanics question requiring standard energy/power formulas. Part (i) uses work-energy theorem with KE change plus PE change. Part (ii) applies P=Fv at constant speed where driving force equals resistance. Both parts are direct applications of standard A-level mechanics principles with no problem-solving insight required, making it slightly easier than average. |
| Spec | 6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component6.02l Power and velocity: P = Fv |
7 A car has mass 800 kg .\\
(i) The car accelerates from $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ to $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in climbing a hill with a vertical height of 16 m . Ignoring resistive forces, find the work done by the engine.\\
(ii) The engine produces a constant power output of 189 kW . The car now travels along horizontal ground. Modelling the resistive force as $7 v ^ { 2 } \mathrm {~N}$, where $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is the speed, find the value of $v$ for which the speed of the car is constant.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2018 Q7}}