Question

what does this graph represent?
an object moving with constant velocity
an object moving with constant acceleration
an object at rest
an object moving with a negative velocity

Explanation:

Step1: Analyze the position - time graph

In a position - time graph, the slope of the graph gives the velocity. 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: Calculate the slope

For the given graph, \(\Delta x = 0\) (since the position does not change with time). So, \(m=\frac{0}{\Delta t}=0\).

Step3: Relate slope to motion

A slope of \(0\) in a position - time graph means that the velocity \(v = 0\). When the velocity of an object is \(0\), the object is at rest.

For an object moving with constant velocity, the position - time graph is a straight line with a non - zero slope (\(v=\frac{\Delta x}{\Delta t}=\text{constant}
eq0\)). For an object moving with constant acceleration, the position - time graph is a parabola (\(x = x_0+v_0t+\frac{1}{2}at^{2}\), which is a quadratic function). For an object moving with negative velocity, the slope of the position - time graph is negative (\(v=\frac{\Delta x}{\Delta t}<0\))

Answer:

an object at rest