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**Unformatted text preview: **x , with respect to time, t ; that is d 2 x dt 2 = a. Integrating both sides with respect to t and using the given fact that a is constant we obtain dx dt = at + C. (1.1) The instantaneous velocity, v , of an object is given by the rst derivative of distance, x , with respect to time, t . At the beginning of the race, t = 0, both racers have zero velocity. Therefore we have C = 0. Integrating equation (1.1) with respect to t we obtain x = 1 2 at 2 + C 1 . or this problem we will use the starting position for both competitors to be x = 0 at t = 0. Therefore, we have C 1 = 0. This gives us a general equation used for both racers as x = 1 2 at 2 or t = r 2 x a , 2...

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