1. What is Velocity?

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, including both magnitude (speed) and direction. Unlike speed, which is scalar, velocity provides information about the direction of motion.

2. How Does the Calculator Work?

The calculator uses the velocity formula:

Where:

• \( \vec{v} \) — Velocity vector (m/s)
• \( s \) — Speed magnitude (m/s)
• \( \hat{d} \) — Unit direction vector

Explanation: The calculator converts the direction angle to a unit vector and multiplies it by the speed magnitude to obtain the velocity vector components.

3. Importance of Velocity Calculation

Details: Velocity calculation is essential in physics, engineering, navigation, and many other fields where both the magnitude and direction of motion are important for analysis and prediction.

4. Using the Calculator

Tips: Enter speed in meters per second (m/s) and direction in degrees (0° = positive x-axis, 90° = positive y-axis). All values must be valid (speed > 0).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between speed and velocity?
A: Speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude and direction).

Q2: How is direction measured in this calculator?
A: Direction is measured in degrees from the positive x-axis (0°), with positive angles measured counterclockwise.

Q3: What are typical velocity units?
A: The SI unit is meters per second (m/s), but other units like km/h or mph can be converted accordingly.

Q4: Can velocity be negative?
A: Velocity components can be negative, indicating direction opposite to the positive coordinate axis.

Q5: How is velocity used in real-world applications?
A: Velocity is used in navigation systems, projectile motion analysis, fluid dynamics, vehicle dynamics, and many other engineering and scientific applications.