An object moves in the positive x-direction at a speed of 40 m/s. As it passes through the origin, it starts to experience a constant acceleration of 3.5 m/s2 in the negative x-direction. How much time elapses before the object returns to the origin

11,429 seconds.

Step-by-step explanation: Initially, the object is moving away from the origin in the positive x-direction but decelerating at constant rate until it reaches rest and then, the objects returns to the origin with a constant acceleration. By substituting the position equation of an object accelerating at constant rate, the following expression is found:

Which is a second-order polynomial. The time can be found easily by applying the General Second-Grade Equation, whose two roots are presented below:

The second roots contains the answer.