The day after the incident described in Problem 44, the instructor finds herself in the same situation. This time, she tries a harder physics exercise. She keeps running at a constant \(6.0 \mathrm{~m} / \mathrm{s}\) after drawing even with the bus door and pulls ahead for a while, but the accelerating bus soon overtakes her. By what maximum distance does she get ahead of the door?

Data from Problem 44

As a physics instructor hurries to the bus stop, her bus passes her, stops ahead, and begins loading passengers. She runs at \(6.0 \mathrm{~m} / \mathrm{s}\) to catch the bus, but the door closes when she's still \(8.0 \mathrm{~m}\) behind the door, and the bus leaves the stop at a constant acceleration of \(2.0 \mathrm{~m} / \mathrm{s}^{2}\). She has missed her bus, but as a physics exercise she keeps running at \(6.0 \mathrm{~m} / \mathrm{s}\) until she draws even with the bus door.

(a) Calculate \(\Delta t\) from the instant the bus leaves the stop to the instant the instructor draws even with the door.

(b) At the instant she draws even, how fast is she moving?

(c) At the instant she draws cven, how fast is the bus moving?

(d) Plot \(v(t)\) for the bus and the instructor.

(e) Plot \(x(t)\) for the bus and the instructor.