Question

1. on which type of graph does the slope of the line represent the acceleration of the object?

a straight diagonal line on a speed - versus - time graph
a straight diagonal line on a distance - versus - time graph
a curved line on a speed - versus - time graph
a curved line on a distance - versus - time graph

Explanation:

• For speed - versus - time graph:
• The formula for acceleration \(a=\frac{\Delta v}{\Delta t}\). In a speed - versus - time (\(v - t\)) graph, the slope of the line is calculated as \(\text{slope}=\frac{\Delta v}{\Delta t}\), which is exactly the formula for acceleration. A straight diagonal line on a \(v - t\) graph implies a constant acceleration (\(\frac{\Delta v}{\Delta t}=\text{constant}\)).
• A curved line on a \(v - t\) graph implies a non - constant acceleration (\(\frac{\Delta v}{\Delta t}\) is changing).
• For distance - versus - time graph:
• The formula for speed \(v = \frac{\Delta d}{\Delta t}\). In a distance - versus - time (\(d - t\)) graph, the slope of the line is \(\text{slope}=\frac{\Delta d}{\Delta t}\), which represents the speed of the object. A straight diagonal line on a \(d - t\) graph implies a constant speed (\(\frac{\Delta d}{\Delta t}=\text{constant}\)), and a curved line on a \(d - t\) graph implies a non - constant speed.

Answer:

a straight diagonal line on a speed - versus - time graph