Question

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

Answer 1

Step-by-step explanation:

Below is an attachment containing the solution.

Answer 2

Answer: 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:

$0 = 0 + (40 m/s)\cdot{t}+\frac{1}{2}\cdot{-3.5\frac{m}{s^{2}}\cdot{t}^{2}$

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:

$t_{1} = 0, t_{2} \approx 11,429$

The second roots contains the answer.