Displacement and Velocity Quiz with Answer Key

📚 Quick Study Guide

• 📏 Displacement: The change in position of an object. It's a vector quantity, meaning it has both magnitude and direction. Denoted as $\Delta x = x_{final} - x_{initial}$.
• ⏱️ Time Interval: The duration over which displacement occurs, denoted as $\Delta t = t_{final} - t_{initial}$.
• 🏃 Velocity: The rate at which an object changes its position. Average velocity is defined as $\bar{v} = \frac{\Delta x}{\Delta t}$. It's also a vector quantity.
• 🧭 Speed: The magnitude of velocity, without considering direction. It's a scalar quantity.
• ➕ Positive & Negative Velocity: Positive velocity indicates movement in the positive direction; negative velocity indicates movement in the negative direction.
• 📊 Graphical Representation: Displacement and velocity can be represented on position-time graphs, where the slope of the line represents the velocity.
• 💡 Instantaneous Velocity: Velocity at a specific moment in time. It's the limit of average velocity as the time interval approaches zero: $v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}$.

🧪 Practice Quiz

1. A car travels 20 meters east and then 30 meters west. What is the car's displacement?

   1. 10 meters east
   2. 50 meters west
   3. 10 meters west
   4. 50 meters east

2. A runner completes one lap around a 400-meter track. What is the runner's displacement?

   1. 400 meters
   2. 200 meters
   3. 0 meters
   4. 800 meters

3. A bicycle travels 12 meters in 3 seconds. What is its average velocity?

   1. 36 m/s
   2. 4 m/s
   3. 9 m/s
   4. 15 m/s

4. A train moves at a constant velocity of 25 m/s. How far will it travel in 2 minutes?

   1. 50 meters
   2. 3000 meters
   3. 12.5 meters
   4. 5000 meters

5. An object's initial position is at x = 5 meters, and its final position is at x = -3 meters. What is its displacement?

   1. 8 meters
   2. -8 meters
   3. 2 meters
   4. -2 meters

6. If a car's velocity changes from 10 m/s to 30 m/s in 5 seconds, what is its average acceleration?

   1. 2 m/s²
   2. 4 m/s²
   3. 6 m/s²
   4. 8 m/s²

7. A ball is thrown upwards and reaches its highest point. What is its instantaneous velocity at the highest point?

   1. 9.8 m/s
   2. -9.8 m/s
   3. 0 m/s
   4. It depends on the initial velocity.