Question

Suppose suppose a car has 17 inch rim , and the center of rotation of the wheel sits 19 inches from the ground, and the car is driving at a constant speed of 100 mph ; the position of a point on the edge of the rim can be parametrized by the prolate cycloid.

r(t) = 〈19 ω t - 17 sin(ω t), 19 - 17 cos(ω t)〉.

Is this a constant speed curve? If not, find the highest speed attained; the speed is certainly periodic , so it is enough to consider a single revolution. In other words, when is this point on the rolling wheel moving fastest, or does it move at a constant speed?

Answer 1