Question

1. which graph shows an object with positive acceleration? (look at the axis labels carefully)

Explanation:

Step1: Recall the formula for acceleration

Acceleration \(a=\frac{\Delta v}{\Delta t}\), where \(\Delta v = v_{f}-v_{i}\) and \(\Delta t=t_{f} - t_{i}\)

Step2: Analyze the distance - time graph (Graph A)

In a distance - time graph, a horizontal line means \(\frac{\Delta d}{\Delta t}=0\) (constant distance, object is at rest). So acceleration \(a = 0\)

Step3: Analyze the constant velocity graph (Graph B)

In a velocity - time graph, a horizontal line means \(\frac{\Delta v}{\Delta t}=0\) (constant velocity). So acceleration \(a = 0\)

Step4: Analyze the increasing velocity graph (assuming Graph C)

In a velocity - time graph, if the slope \(\frac{\Delta v}{\Delta t}>0\) (velocity is increasing with time). Then, using the formula \(a=\frac{\Delta v}{\Delta t}\), we have \(a>0\) (positive acceleration)

Answer:

C (assuming the third graph is the velocity - time graph with a positive slope)