Question

One day, you got an email from DMV telling you that you have exceeded the speed limit on a highway and demand that you pay the fine. They said that you first passed one of their radar speedometer with a speed of and after , you passed the other radar speedometer and they recorded your speed to be . The radar speedometer is placed every .  The speed limit on the highway was . How can the DMV prove that you violated the speed limit provided that your recorded speed was less than ? 

Hint: Assume that the position function of the distances you traveled was differentiable and continuous.