Instantaneous speed and velocity | One-dimensional motion | Physics | Khan Academy

Introduction

This tutorial focuses on understanding instantaneous speed and velocity within the context of one-dimensional motion in physics. By learning these concepts, you will gain insights into how motion is measured and analyzed, which is fundamental for further studies in physics.

Step 1: Understanding Instantaneous Speed

• Definition: Instantaneous speed is the speed of an object at a specific moment in time.
• Calculation: It can be approximated by measuring the distance traveled over a very short time interval.
• Practical Example:
  • Imagine a car moving along a straight road. If you measure how far the car travels in a fraction of a second, you can calculate its instantaneous speed.
• Formula:
  • Instantaneous speed can be represented mathematically as: [ v = \lim_{\Delta t \to 0} \frac{\Delta d}{\Delta t} ] where ( v ) is the instantaneous speed, ( \Delta d ) is the small displacement, and ( \Delta t ) is the small time interval.

Step 2: Understanding Instantaneous Velocity

• Definition: Instantaneous velocity includes both speed and direction. It indicates how fast and in which direction an object is moving at a specific moment.
• Measurement: Just like speed, instantaneous velocity is calculated over an infinitesimally small time interval.
• Practical Example:
  • If a car is moving northward at 60 km/h, its instantaneous velocity is 60 km/h north.
• Formula:
  • The formula is similar to that of speed: [ v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} ] where ( \Delta x ) represents the small change in position.

Step 3: Distinguishing Between Speed and Velocity

• Key Differences:
  • Speed is a scalar quantity (only magnitude).
  • Velocity is a vector quantity (magnitude and direction).
• Practical Tip:
  • Always consider direction when discussing velocity. For example, saying "50 km/h" provides speed, while "50 km/h east" provides velocity.

Step 4: Real-World Applications

• Driving: Understanding instantaneous speed helps drivers gauge their speed for safety and compliance with speed limits.
• Sports: Athletes can analyze instantaneous velocity to improve performance.
• Engineering: Engineers use these concepts in designing vehicles and machinery to ensure proper functionality at various speeds.

Conclusion

In this tutorial, we explored the concepts of instantaneous speed and velocity, emphasizing their definitions, calculations, and real-world applications. Understanding these fundamentals is crucial for further studies in physics and practical applications in everyday life. To deepen your knowledge, consider exploring position vs. time graphs, as mentioned in the Khan Academy resources.