Question

An object is moving in the plane according to these parametric equations:
x(t) = πt + cos(4πt + π/2)
y(t) = sin(4πt + π/2)
A portion of the "cycloidal" path (on the time interval [0,1]) is shown in this figure:
The first time the tangent line is vertical will be t=
Incorrect: Your answer is incorrect.


(f) The second time the tangent line is vertical will be t=

(g) What is the maximum horizontal velocity?
(h) What is the minimum horizontal velocity?
(i) The speed of the object at time t is s(t)=