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Answer 1 · 2016-08-25T11:46:43

#v =4.29163["m/s"]#

The point #p={x,y}# given by

#p = {(t+1)cos(alpha t + pi/2),(t+1)sin(alpha t+pi/2)}# describes the point #A# path.

Here we will assume #alpha = 1#. This path, begins for #t = 0# in

#p_i = {0,1}# and after a time #t_f = 2pi#, the point #A# location is
#p_f = {0,2pi+1}#

The path lenght is given by

#d = int_0^(t_f)ds = int_0^(2pi)sqrt((dx/dt)^2+(dy/dt)^2)dt# so

#d = int_0^(t_f)(sqrt(t^2+2t+2))dt# which gives

#d=26.9651#

but #v = d/(t_f)=4.29163["m/s"]#

Attached a figure showing the point #A# path.

enter image source here