2. The Batmobile travels in a straight line such that t seconds after passing through Arkham, its velocity v(t) in meters per second is given by v(t) = 5t³ + (20 – 30k)t² – 100kt + 200k + 50 where k is constant. (a) Find an expression for the acceleration of the Batmobile in terms of k and t. (b) Suppose that the acceleration of the Batmobile five seconds after passing through Arkham is 175 m/s?. Determine the value of k five seconds after passing through Arkham. (c) Using the value of k from item (b), find the range of values of t for which the Batmobile is accelerating positively. (d) Using the value of k from item (b), determine the values of t when the Batmobile is accelerating at its fastest and slowest within six seconds of passing through Arkham.

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