Question

(underline) negative negative negative negative
speed (underline) speeding up slowing down speeding up slowing down speeding up slowing down speeding up slowing down
graph four velocity vs. time graphs
acceleration (underline) positive negative positive negative positive negative positive negative

1. acceleration is the change of velocity over time (the slope of a velocity vs. time graph).

explain how you determined whether acceleration is positive or negative using the velocity vs. time graphs.

Explanation:

To determine acceleration's sign from a velocity - time graph, we use the slope of the graph. The formula for slope (which represents acceleration, \(a=\frac{\Delta v}{\Delta t}\)) is used. If the line on the velocity - time graph is increasing (going up from left to right), the slope is positive, so acceleration is positive. This is because as time (\(t\)) increases, velocity (\(v\)) also increases (\(\Delta v>0\) and \(\Delta t > 0\), so \(\frac{\Delta v}{\Delta t}>0\)). If the line is decreasing (going down from left to right), the slope is negative, so acceleration is negative. Here, \(\Delta v<0\) while \(\Delta t>0\), so \(\frac{\Delta v}{\Delta t}<0\). For a horizontal line, the slope is zero, meaning acceleration is zero as \(\Delta v = 0\).

Answer:

To determine if acceleration is positive or negative from a velocity - time graph, we analyze the slope of the graph (since \(a=\frac{\Delta v}{\Delta t}\), the slope of \(v - t\) graph is acceleration). If the velocity - time graph line has a positive slope (the line rises from left to right, so \(\Delta v>0\) as \(\Delta t>0\), making \(a=\frac{\Delta v}{\Delta t}>0\)), acceleration is positive. If the line has a negative slope (the line falls from left to right, so \(\Delta v < 0\) as \(\Delta t>0\), making \(a=\frac{\Delta v}{\Delta t}<0\)), acceleration is negative. A horizontal line (slope = 0) means acceleration is zero.