T_p
=
\int _{0}^{\pi {\lambda \over v}} }\! \sqrt{({dt_p \over dq})^2-{({dx_p \over dq})^2 \over c^2}} {dq}
=
\int _{0}^{\pi {\lambda \over v}} }\! {dq}=\pi {\lambda \over v}