Question

select the correct answer. the motion of a car on a position-time graph is represented with a horizontal line. what does this indicate about the car’s motion? a. it’s not moving. b. it’s moving at a constant speed. c. it’s moving at a constant velocity. d. it’s speeding up.

Explanation:

In a position - time graph, the slope of the line represents the velocity (or speed, in the case of magnitude) of the object. The formula for the slope (which gives velocity) is $v=\frac{\Delta x}{\Delta t}$, where $\Delta x$ is the change in position and $\Delta t$ is the change in time. For a horizontal line, the change in position $\Delta x = 0$ (since the $y$ - value, which represents position, does not change as time $t$ (the $x$ - value) changes). If $\Delta x = 0$, then from the velocity formula $v=\frac{\Delta x}{\Delta t}$, the velocity $v = 0$. This means the object is not moving.

• Option B: A constant speed would be represented by a straight line with a non - zero constant slope (not a horizontal line).
• Option C: A constant velocity (which includes both speed and direction) would also be a straight line with a non - zero constant slope (not horizontal).
• Option D: Speeding up would be represented by a line with an increasing slope (curved or a line with changing slope), not a horizontal line.

Answer:

A. It's not moving