1. What is the Distance Formula?

The distance formula \( s = \frac{(v + u)t}{2} \) calculates the distance traveled by an object when its velocity changes uniformly from initial velocity \( u \) to final velocity \( v \) over time \( t \). This formula is derived from the concept of average velocity.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( s \) — Distance traveled (meters)
• \( v \) — Final velocity (m/s)
• \( u \) — Initial velocity (m/s)
• \( t \) — Time duration (seconds)

Explanation: The formula calculates distance by multiplying the average velocity \( \frac{v + u}{2} \) by the time taken \( t \).

3. Importance of Distance Calculation

Details: This calculation is fundamental in physics for analyzing motion, solving kinematics problems, and understanding relationships between velocity, time, and displacement in uniformly accelerated motion.

4. Using the Calculator

Tips: Enter final velocity in m/s, initial velocity in m/s, and time in seconds. All values must be valid (time > 0). The calculator will compute the distance traveled.

5. Frequently Asked Questions (FAQ)

Q1: When is this formula applicable?
A: This formula applies to motion with constant acceleration, where velocity changes uniformly over time.

Q2: What if acceleration is not constant?
A: For non-uniform acceleration, this formula doesn't apply. You would need to use calculus methods or other kinematic equations.

Q3: Can this formula be used for deceleration?
A: Yes, deceleration is simply negative acceleration. The formula works as long as the velocity changes uniformly.

Q4: What are the SI units for this calculation?
A: Velocity in meters per second (m/s), time in seconds (s), and distance in meters (m).

Q5: How does this relate to other kinematic equations?
A: This is one of the standard kinematic equations that can be derived from the basic definitions of velocity and acceleration.