Question

17 use the position time graph below to answer the question. position vs. time position (m) time (s) which line segment represents positive acceleration? a de b cd c bc d ab

Explanation:

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

In a position - time graph, the slope of the graph gives the velocity. Acceleration is the rate of change of velocity. If the slope (velocity) is increasing, there is a positive acceleration.

Step2: Analyze each segment

• Segment \(AB\):

The slope of the position - time graph (which represents velocity) is increasing. As time increases, the change in position (\(\Delta x\)) per unit time (\(\Delta t\)) is getting larger. Mathematically, if \(v=\frac{\Delta x}{\Delta t}\), and \(v\) is increasing, then \(a = \frac{\Delta v}{\Delta t}>0\) (since \(a=\frac{d v}{d t}\) and \(v\) is increasing).

• Segment \(BC\):

The slope of the position - time graph (velocity) is constant. If \(v = \text{constant}\), then \(a=\frac{\Delta v}{\Delta t}=0\) (because \(\Delta v = 0\)).

• Segment \(CD\):

The slope of the position - time graph (velocity) is \(0\) (horizontal line). So, \(a=\frac{\Delta v}{\Delta t}=0\) (since \(v\) does not change).

• Segment \(DE\):

The slope of the position - time graph (velocity) is negative and constant. If \(v=\text{constant}\) (negative), then \(a = \frac{\Delta v}{\Delta t}=0\)

Answer:

D. \(AB\)