Nikon D 750 Refurbed $ 1249 . true <| sep |> I know i was saying that the ack ack was another part of the joke and not just the the bond <| sep |> Jesus comes back to rule the earth from Jerusalem . Known as the Thousand year millennial reign <| sep |> Same problem here on iOS . <| sep |> As it turns out , it doesn ' t matter . By the premise of the problem , no matter how you cycle , you will have to ensure that the integral of vt from 0 to T is less than X . I am making the hopefully reasonable assumption that vt 0 , i . e . you are not stopping and going against traffic , so this condition is sufficient . But as it turns out , the expected value of speed after the light turns green is exactly the integral of vt from 0 to T over T . So it turns out that as long as you plan your speed such that in a hypothetically maximal red light , you end up at the light , your expected value of speed is XT . I guess a slight caveat if we also enforce no speeding up , your speed is also bounded by V . Other considerations If you want to minimize the maximum absolute acceleration , you should have constant acceleration from V to 2 XTV for a constant acceleration of 2 XT 2 VT . If you want to mimimize the square of the difference of speed from your current speed and V say it ' s your top speed , you should immediately decelerate to the point where you can ride at a constant rate of XT .