Question

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 stationary.

the slope of the line is positive, and the object will be stationary.

the slope of the line is equal to zero and the object will be in motion.

the slope of the line is negative, and the object will be stationary.

Explanation:

In a time - position graph, the slope of the line represents the velocity of the object. If the velocity is constant and the object is stationary, the position of the object does not change with time. So, the change in position ($\Delta y$) is zero. The slope of a line in a graph is calculated as $\text{slope}=\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in position and $\Delta x$ is the change in time. If $\Delta y = 0$, the slope is zero. And if the object is stationary, its velocity is zero (which is a constant velocity). Let's analyze each option:

• Option 1: The slope of the line is equal to zero (since $\Delta y = 0$ for a stationary object) and the object will be stationary. This is correct.
• Option 2: A positive slope would mean the object is moving (since slope = velocity), so it can't be stationary. Eliminate this option.
• Option 3: If the object is in motion, the position is changing with time, so $\Delta y

eq0$ and the slope (velocity) would not be zero. Eliminate this option.

• Option 4: A negative slope would mean the object is moving (in the opposite direction), so it can't be stationary. Eliminate this option.

Answer:

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