Question

position, distance, and displacement quick check
imagine a time - position graph where the velocity of an object is constant. what will be observed on the graph concerning the slope of the line segment as well as the velocity of the object?
(1 point)
the slope of the line is equal to zero and the object will be in motion.
the slope of the line is equal to zero and the object will be stationary.
the slope of the line is negative, and the object will be stationary.
the slope of the line is positive, and the object will be stationary.

Explanation:

1. Recall the concept of a time - position graph: In a time - position (or position - time) graph, the slope of the line segment is given by the formula $slope=\frac{\Delta position}{\Delta time}$, and velocity $v = \frac{\Delta x}{\Delta t}$, where $\Delta x$ is the change in position and $\Delta t$ is the change in time. So, the slope of the position - time graph is equal to the velocity of the object.
2. Analyze the case when velocity is constant and the object is stationary: If an object is stationary, its position does not change with time, i.e., $\Delta x = 0$. Then, the slope $=\frac{\Delta x}{\Delta t}=\frac{0}{\Delta t}=0$ (for $\Delta t

eq0$). And if the velocity is constant and the object is stationary, the velocity $v = 0$, which matches the slope being zero.

1. Eliminate other options:

• For the option "The slope of the line is equal to zero and the object will be in motion": If an object is in motion with constant velocity, the slope (which is velocity) should be non - zero (positive or negative depending on direction), so this is incorrect.
• For the option "The slope of the line is negative, and the object will be stationary": A negative slope would imply a non - zero velocity (negative velocity), but a stationary object has velocity zero, so this is incorrect.
• For the option "The slope of the line is positive, and the object will be stationary": A positive slope would imply a non - zero velocity (positive velocity), but a stationary object has velocity zero, so this is incorrect.

Answer:

The slope of the line is equal to zero and the object will be stationary.