Answer to Question #242368 in Classical Mechanics for louryy

Question

As a physics instructor hurries to the bus stop, her bus passes her, stops ahead, and begins loading passengers. She runs at 6.0 m/s to catch the bus, but the door closes when she's still 6.0 m behind the door, and the bus leaves the stop at a constant acceleration of 2.0 m/s2 . She has missed her bus, but as a physics exercise she keeps running at 6.0 m/s until she draws even with the bus door. She keeps running at a constant 6.0 m/s after drawing even with the bus door and pulls ahead for a while, but the accelerating bus soon overtakes her. Calculate Δt

Δt from the instant the bus leaves the stop to the instant the instructor draws even with the door.

Answer 1

The initial distance between the door and the instructor is 6 m. The distance for the bus traveling at 2 m/s² between the initial location of the instructor and the place where it overtook her:

$$D=d_0+\frac{at^2}2.$$

The distance the instructor covers at a constant speed of 6 m/s:

$$D=vt,\\\space\\ \frac{at^2}2-vt+d_0=0 ,\\\space\\ t=4.73\text{ s}.$$