Solved Examples of Acceleration vs. Time Graphs: Constant Acceleration

📚 Quick Study Guide

• 📈 Acceleration vs. Time Graphs: These graphs plot acceleration on the y-axis and time on the x-axis. For constant acceleration, the graph is a horizontal line.
• 📏 Area Under the Curve: The area under an acceleration vs. time graph represents the change in velocity ($\Delta v$).
• 🧮 Constant Acceleration: This means the acceleration remains the same over time. In other words, there is no change in acceleration.
• ➕ Calculating Change in Velocity: $\Delta v = a \cdot \Delta t$, where $a$ is the constant acceleration and $\Delta t$ is the change in time.
• 🧭 Interpreting the Graph: A horizontal line above the x-axis indicates positive constant acceleration, while a line below indicates negative constant acceleration (deceleration). A line on the x-axis means zero acceleration (constant velocity).

Practice Quiz

1. A car accelerates constantly at 2 m/s² for 5 seconds. What is the change in velocity?

   1. 5 m/s
   2. 7 m/s
   3. 10 m/s
   4. 2.5 m/s

2. What does the area under an acceleration vs. time graph represent?

   1. Displacement
   2. Velocity
   3. Change in velocity
   4. Acceleration

3. A horizontal line at y = -3 m/s² on an acceleration vs. time graph indicates:

   1. Constant velocity
   2. Constant acceleration of 3 m/s²
   3. Constant deceleration of 3 m/s²
   4. Increasing acceleration

4. If the acceleration is zero, what does the acceleration vs. time graph look like?

   1. A horizontal line above the x-axis
   2. A horizontal line below the x-axis
   3. A horizontal line on the x-axis
   4. A diagonal line

5. An object's velocity changes from 10 m/s to 20 m/s in 5 seconds with constant acceleration. What is the acceleration?

   1. 1 m/s²
   2. 2 m/s²
   3. 3 m/s²
   4. 4 m/s²

6. What is the shape of an acceleration vs. time graph for constant acceleration?

   1. Parabola
   2. Hyperbola
   3. Straight Line
   4. Horizontal Line

7. If the area under an acceleration vs. time graph is 15 m/s, what does this value represent?

   1. The final velocity
   2. The initial velocity
   3. The change in velocity
   4. The displacement