Question

question 19 (1 point)
if the position versus time graph of an object is a vertical line, the object is
moving with constant non - zero speed.
moving with constant non - zero acceleration.
at rest.
moving with infinite speed.

Explanation:

1. Recall the formula for speed from a position - time graph: The speed \(v\) of an object is given by the slope of the position - time graph, where \(v=\frac{\Delta x}{\Delta t}\), with \(\Delta x\) being the change in position and \(\Delta t\) being the change in time.
2. Analyze a vertical line on a position - time graph: For a vertical line, the change in time \(\Delta t = 0\) (since the time coordinate does not change as we move along the vertical line), while the change in position \(\Delta x\) is non - zero (because the position changes while time remains the same).
3. Calculate the speed: Substituting into the speed formula \(v = \frac{\Delta x}{\Delta t}\), if \(\Delta t=0\) and \(\Delta x

eq0\), then \(v=\frac{\Delta x}{0}\), which is undefined in the real number system, but in the context of the limit (as \(\Delta t\) approaches 0), the speed approaches infinity.

• For the option "moving with constant non - zero speed", a constant non - zero speed would correspond to a straight line with a non - zero slope (not a vertical line).
• For the option "moving with constant non - zero acceleration", a position - time graph for constant acceleration is a parabola (not a vertical line).
• For the option "at rest", an object at rest has a position - time graph with a slope of 0 (a horizontal line), not a vertical line.

Answer:

D. moving with infinite speed