Velocity Calculator

How to Use the Velocity Calculator

The Velocity Calculator solves motion problems using the fundamental relationship between distance, speed, and time. It handles both uniform motion (constant speed) and uniformly accelerated motion, making it suitable for physics problems from basic to intermediate level.

Uniform Motion (Constant Speed)

The basic formula is: Distance = Speed × Time (d = v × t). Enter any two values to find the third. A car traveling at 60 mph for 2.5 hours covers 60 × 2.5 = 150 miles. Running 10 km in 50 minutes means a speed of 12 km/h.

Accelerated Motion

For objects speeding up or slowing down with constant acceleration, the calculator uses the kinematic equations:

v = v₀ + a × t (final velocity from initial velocity, acceleration, and time)

d = v₀ × t + ½ × a × t² (distance traveled under acceleration)

v² = v₀² + 2 × a × d (final velocity from initial velocity, acceleration, and distance)

Practical Examples

A car accelerates from 0 to 60 mph (26.8 m/s) in 8 seconds. Acceleration = 26.8/8 = 3.35 m/s². Distance covered during acceleration = ½ × 3.35 × 64 = 107.2 m. A dropped object falls with acceleration 9.8 m/s². After 3 seconds: velocity = 29.4 m/s, distance fallen = 44.1 m.

Unit Conversions

The calculator supports multiple unit systems. Speed in m/s, km/h, mph, ft/s, or knots. Distance in meters, kilometers, miles, or feet. Time in seconds, minutes, or hours. Acceleration in m/s², ft/s², or g-force (1g = 9.8 m/s²).

Frequently Asked Questions

Q: What is the difference between speed and velocity?

A: Speed is a scalar (magnitude only): how fast something moves. Velocity is a vector (magnitude and direction): how fast and in what direction. A car going 60 mph has a speed of 60 mph. Going 60 mph north is a velocity. For calculations involving only magnitude, they are interchangeable.

Q: How do I calculate average speed for a trip with multiple segments?

A: Average speed = total distance / total time. If you drive 60 miles at 30 mph (2 hours) then 60 miles at 60 mph (1 hour), total distance is 120 miles in 3 hours, so average speed is 40 mph. Note: it is not simply (30+60)/2 = 45 mph because you spend more time at the slower speed.

Q: What is terminal velocity?

A: Terminal velocity is the maximum speed an object reaches when falling through a fluid (like air), where air resistance equals gravitational force and acceleration becomes zero. For a skydiver, terminal velocity is about 120 mph (54 m/s) in a belly-down position. This calculator assumes no air resistance for its kinematic equations.