To determine the position of the object when its velocity is zero, we can use the equations of motion in one dimension. In this case, we have constant acceleration and an initial velocity. The relevant equation is:
v² = u² + 2as
Where: v is the final velocity (zero in this case), u is the initial velocity (-24 m/s), a is the acceleration (6 m/s²), s is the displacement (position we want to find).
Since we're looking for the position when velocity is zero, we can rearrange the equation as follows:
0 = (-24)² + 2(6)(s)
Simplifying the equation gives us:
0 = 576 + 12s
Rearranging further:
12s = -576
Dividing both sides by 12:
s = -576 / 12
s = -48
Therefore, when the velocity of the object is zero, its position along the x-axis is -48 meters.