Moderate -0.5 This question only asks students to translate a worded statement into a differential equation (dr/dt = k/r), which is a straightforward application of 'inversely proportional' language. No solving or further manipulation is required, making it easier than average but not trivial since it does require understanding the relationship between rate of change and inverse proportionality.
7 When a stone is dropped into still water, ripples move outwards forming a circle of rippled water. At time \(t\) seconds after the stone hits the water the radius of the circle of ripples is increasing at a rate that is inversely proportional to the radius When the radius is 200 cm the rate of increase of the radius is 5 cm per second.
Write down the differential equation that represents this situation.
7 When a stone is dropped into still water, ripples move outwards forming a circle of rippled water. At time $t$ seconds after the stone hits the water the radius of the circle of ripples is increasing at a rate that is inversely proportional to the radius When the radius is 200 cm the rate of increase of the radius is 5 cm per second.
Write down the differential equation that represents this situation.
\hfill \mbox{\textit{OCR MEI C4 Q7 [4]}}