3. A cyclist and her cycle have a combined mass of 75 kg . The cyclist is cycling up a straight road inclined at \(5 ^ { \circ }\) to the horizontal. The resistance to the motion of the cyclist from non-gravitational forces is modelled as a constant force of magnitude 20 N . At the instant when the cyclist has a speed of \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), she is decelerating at \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Find the rate at which the cyclist is working at this instant. When the cyclist passes the point \(A\) her speed is \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At \(A\) she stops working but does not apply the brakes. She comes to rest at the point \(B\). The resistance to motion from non-gravitational forces is again modelled as a constant force of magnitude 20 N .
2. Use the work-energy principle to find the distance \(A B\).