An object moves in the +x direction at a speed of 30 m/s. As it passes through the origin, it starts to experience a constant acceleration of 3.7 m/s2 in the -x direction.

(b) How much time elapses before the object returns to the origin?


_____________s

this is like a projectile problem turned sideways

0 = -(.5 * 3.7 * t^2) + (30 * t)

solve the quadratic for t (you want the non-zero solution)

To find the time it takes for the object to return to the origin, we can use the equations of motion. The equation that relates displacement, initial velocity, acceleration, and time is:

x = x0 + v0t + (1/2)at^2

In this case, the initial velocity (v0) is 30 m/s, the acceleration (a) is -3.7 m/s^2, the displacement (x) is 0 (since it returns to the origin), and the initial position (x0) is also 0 (since it starts at the origin).

Plugging in the values, we get:

0 = 0 + 30t + (1/2)(-3.7)t^2

Simplifying the equation, we get:

0 = 30t - (1.85)t^2

Rearranging the equation, we get a quadratic equation:

(1.85)t^2 - 30t = 0

Now, we can solve this equation for t by factoring it or using the quadratic formula:

(1.85)t(t - 16.22) = 0

This gives us two possible solutions: t = 0 and t = 16.22 s.

However, since we are interested in the time it takes for the object to return to the origin, we discard the t = 0 solution and consider only the positive value.

Therefore, the time it takes for the object to return to the origin is approximately 16.22 seconds.