A point moves in the plane `xy` according to the law `x = alpha sin omega t, y = alpha(1 - cos omega t)`, where `alpha` and `omega` are positive constant and `t` is time. Find the distance traversed by point in time `t_(0)`.

Explanation

`x = alpha sin omega t`
`v_(x) = (d x)/(d t) = alpha = cos omega t . Omega = alpha omega = cos omega t`
`y = alpha(1 - cos omega t)`
`v_(y) = (d y)/(d t) = alpha[0 - (- sin omega t)omega] = alpha omega sin omega t`
`v = sqrt(v_(x)^(2) + v_(y)^(2)) = alpha omega = constant`
Distance in time `t_(0)`
`s = v t_(0)`
`= alpha omega t_(0)`