Question

here are two position vs time graph... what does graph a represent? practice a practice b

Explanation:

Step1: Analyze the slope of the graph

The slope of a position - time graph represents velocity.
For Practice A:
The slope of the graph is increasing with time.
The formula for velocity \(v=\frac{\Delta x}{\Delta t}\) (where \(\Delta x\) is the change in position and \(\Delta t\) is the change in time). As the slope \(\frac{\Delta x}{\Delta t}\) is increasing, the velocity is increasing.
If the acceleration \(a = \frac{\Delta v}{\Delta t}\) (where \(\Delta v\) is the change in velocity) and since \(v\) is increasing, \(a> 0\). So, the object is moving with a positive acceleration.
For Practice B:
The slope of the graph is decreasing with time.
Since \(v=\frac{\Delta x}{\Delta t}\) and the slope is decreasing, the velocity is decreasing.
If \(a=\frac{\Delta v}{\Delta t}\) and \(v\) is decreasing (\(\Delta v<0\)), \(a < 0\). So, the object is moving with a negative acceleration (decelerating)

Answer:

Practice A: The object is moving with a positive acceleration. Practice B: The object is moving with a negative acceleration (decelerating)