Question

9 1.333/2 points multiple answer what does it mean if your position vs. time graph has a negative slope? check all that apply! the object is moving in the negative x - direction. the object is not moving at all. the object has a negative velocity. the object is moving away from the origin. the object has a negative speed. the object is moving back towards the origin

Explanation:

1. For "The object is moving in the negative x - direction": In a position - time graph, the slope represents velocity ($v=\frac{\Delta x}{\Delta t}$). A negative slope means the change in position ($\Delta x$) is negative over time ($\Delta t>0$), so the object is moving in the negative x - direction.
2. For "The object is not moving at all": A zero - slope graph would mean the object is not moving (constant position). A negative slope means the object is moving, so this is incorrect.
3. For "The object has a negative velocity": Velocity is the slope of the position - time graph ($v = \frac{\Delta x}{\Delta t}$). A negative slope implies a negative velocity since $\Delta t$ is always positive (time moves forward), so if $\Delta x$ is negative, velocity is negative.
4. For "The object is moving away from the origin": A negative slope just tells us the direction of motion (negative x - direction), but the object could be moving away from the origin (e.g., if it was at $x=-5$ and moves to $x = - 10$) or towards the origin (e.g., if it was at $x = 5$ and moves to $x=0$). So we can't be sure it's moving away from the origin.
5. For "The object has a negative speed": Speed is the magnitude of velocity, so it is always non - negative. So this is incorrect.
6. For "The object is moving back towards the origin": As explained in the fourth point, a negative slope (negative velocity) doesn't necessarily mean the object is moving towards the origin. It could be moving away from the origin in the negative x - direction.

The correct options are:

• The object is moving in the negative x - direction.
• The object has a negative velocity.

Answer:

• The object is moving in the negative x - direction.
• The object has a negative velocity.