- A cyclist and her cycle have a combined mass of 60 kg . The cyclist is moving along a straight horizontal road and is working at a constant rate of 200 W .
When she has travelled a distance \(x\) metres, her speed is \(v \mathrm {~ms} ^ { - 1 }\) and the magnitude of the resistance to motion is \(3 v ^ { 2 } \mathrm {~N}\).
- Show that \(\frac { \mathrm { d } v } { \mathrm {~d} x } = \frac { 200 - 3 v ^ { 3 } } { 60 v ^ { 2 } }\)
The distance travelled by the cyclist as her speed increases from \(2 \mathrm {~ms} ^ { - 1 }\) to \(4 \mathrm {~ms} ^ { - 1 }\) is \(D\) metres.
- Find the exact value of \(D\)