Question

identifying acceleration on position vs time graphs
which graph shows acceleration?
position (m)
time (s)
position (m)
time (s)
position (m)
time (s)

Explanation:

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

The slope of a position - time graph gives the velocity. If the slope is constant, the velocity is constant and acceleration \(a = 0\). If the slope is changing, the velocity is changing and there is an acceleration.

Step2: Analyze each graph

• For the first graph (a straight - line), the slope \(m=\frac{\Delta x}{\Delta t}\) is constant. So, the velocity \(v\) is constant and \(a = 0\).
• For the second graph (a curved line), the slope \(\frac{\Delta x}{\Delta t}\) is changing. Since \(v=\frac{\Delta x}{\Delta t}\) (velocity) is changing, and \(a=\frac{\Delta v}{\Delta t}\), there is an acceleration.
• For the third graph (a straight - line), the slope \(m = \frac{\Delta x}{\Delta t}\) is constant. So, the velocity \(v\) is constant and \(a=0\).

Answer:

The second graph (the curved - line graph) shows acceleration.