Question

Question #5def0

Answer 1

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

Explanation:

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.