You decide to use a geartrain to connect your motor to your rear axle.Using the constraints below, calculate the minimum number of gear stages (n) needed to accomplish this. Top speed should be reached in final gear at max. RPM. imax (per stage) = 6 vmax = 160 kph nmax = 20000 rpm wheel diameter = 15 inch

Stylized side-view illustration of a vehicle and multi-stage gear train. Three short orange horizontal input strokes enter a large black circular outline on the left. A small red gear inside/adjacent to the black circle meshes with a larger red/blue gear marked by a black central dot. An ellipsis between the first and rightmost gear pairs indicates intervening stages. At the right, a smaller blue/purple gear meshes with a larger green gear inside a gray wheel/tire circle. A bracket beneath the left gear pair is labeled "1"; a bracket beneath the rightmost pair is labeled "n", with "..." between them. A simple driver/head outline, seat and sloping vehicle body are sketched above. No tooth counts, rotation arrows or numerical dimensions are shown.