Solved Examples of Velocity vs. Time Graph Analysis

📚 Quick Study Guide

• 📏 Displacement: The area under the velocity-time curve represents the displacement of the object. If the area is above the x-axis, the displacement is positive; if below, it's negative.
• 📈 Velocity: The y-value of the graph at any given time represents the instantaneous velocity at that time.
• 🧭 Average Velocity: Calculate displacement by finding the total area under the curve and dividing by the total time interval: $v_{avg} = \frac{\Delta x}{\Delta t}$.
• 📉 Acceleration: The slope of the velocity-time graph represents the acceleration of the object. A positive slope indicates positive acceleration, a negative slope indicates negative acceleration (deceleration), and a zero slope indicates constant velocity. $a = \frac{\Delta v}{\Delta t}$
• ⏱️ Instantaneous Acceleration: The slope of the tangent line at a specific point on the velocity-time graph gives the instantaneous acceleration at that time.

Practice Quiz

1. What does the area under a velocity vs. time graph represent?
   1. (A) Acceleration
   2. (B) Displacement
   3. (C) Time
   4. (D) Velocity
2. What does a horizontal line on a velocity vs. time graph indicate?
   1. (A) Constant acceleration
   2. (B) Increasing acceleration
   3. (C) Constant velocity
   4. (D) Decreasing velocity
3. If the velocity vs. time graph is a straight line sloping upwards, what does it represent?
   1. (A) Constant velocity
   2. (B) Constant acceleration
   3. (C) Zero acceleration
   4. (D) Decreasing acceleration
4. A velocity vs. time graph shows a car slowing down. What does the slope of the graph represent?
   1. (A) Positive acceleration
   2. (B) Negative acceleration
   3. (C) Zero acceleration
   4. (D) Constant velocity
5. How can you determine the instantaneous acceleration at a specific time from a velocity vs. time graph?
   1. (A) Find the area under the curve
   2. (B) Find the slope of the tangent at that point
   3. (C) Read the velocity value at that time
   4. (D) Calculate the average velocity
6. An object's velocity vs. time graph is a curve. What does this indicate about its acceleration?
   1. (A) Constant acceleration
   2. (B) Zero acceleration
   3. (C) Changing acceleration
   4. (D) Constant velocity
7. The area below the x-axis on a velocity vs. time graph represents:
   1. (A) Positive displacement
   2. (B) Negative displacement
   3. (C) Zero displacement
   4. (D) Constant velocity