Analyzing Graphs to Find Acceleration
<p>The problem involves analyzing a velocity vs time graph to find acceleration. To find the acceleration from a velocity vs time graph, we calculate the slope of the line, since slope \(\frac{\Delta y}{\Delta x}\) in this context represents acceleration \(\frac{\Delta velocity}{\Delta time}\).</p>
<p>From the graph labeled "velocity vs time," we can see that the line is straight, which indicates a constant acceleration. We need to pick two points from the graph to calculate the slope. We can use the points (2, 100) and (4, 300).</p>
<p>Applying the slope formula:</p>
\[ \text{Slope (acceleration)} = \frac{\Delta velocity}{\Delta time} = \frac{300 \text{ m/s} - 100 \text{ m/s}}{4 \text{ s} - 2 \text{ s}} = \frac{200 \text{ m/s}}{2 \text{ s}} = 100 \text{ m/s}^2 \]
<p>Therefore, the acceleration of the object is \(100 \text{ m/s}^2\).</p>
