Question

look at this position vs time graph. what does it represent?
speed decreasing
constant speed
speed increasing
stopped vehicle

Explanation:

Step1: Recall the relationship between position - time graph and speed

The slope of a position - time graph gives the speed. The formula for the slope \(m=\frac{\Delta x}{\Delta t}\), where \(\Delta x\) is the change in position and \(\Delta t\) is the change in time.

Step2: Analyze the given graph

In the given position - time graph, the graph is a straight line. For a straight - line position - time graph, the slope \(m = \frac{\Delta x}{\Delta t}\) is constant. Let's assume two points \((t_1,x_1)\) and \((t_2,x_2)\) on the line. The slope \(m=\frac{x_2 - x_1}{t_2 - t_1}\). Since the graph is linear (a straight line), for any two intervals \(\Delta t_1\) and \(\Delta t_2\) with corresponding \(\Delta x_1\) and \(\Delta x_2\), the ratio \(\frac{\Delta x_1}{\Delta t_1}=\frac{\Delta x_2}{\Delta t_2}\) (because of the linear nature of the graph).

Answer:

Constant speed