Average Velocity Calculator

What is Average Velocity?

Average velocity is a vector quantity that describes the rate of change of position over a time interval. Unlike speed, velocity includes direction, so it can be positive or negative depending on the direction of travel.

v_avg = Δx / Δt = (x_f - x_i) / (t_f - t_i)

Where:

v_avg = average velocity
Δx = displacement (change in position)
Δt = time interval
x_f = final position
x_i = initial position
t_f = final time
t_i = initial time

Average Velocity vs. Instantaneous Velocity

Average Velocity	Instantaneous Velocity
Calculated over a time interval	Calculated at a specific moment
Measures overall rate of position change	Measures rate of position change at a point
v_avg = Δx / Δt	v = lim_Δt→0 (Δx / Δt) = dx/dt
Can be different from instantaneous velocity at any moment	Equals the slope of the position-time graph at a specific point

Examples of Average Velocity Calculations

Example 1: A car travels 150 meters east in 10 seconds.

Average Velocity = (150 m) / (10 s) = 15 m/s eastward

Example 2: A cyclist rides 5 km north, then turns around and rides 2 km south. The entire journey takes 30 minutes.

Net Displacement = 5 km - 2 km = 3 km north

Time = 30 min = 0.5 hours

Average Velocity = (3 km) / (0.5 h) = 6 km/h northward

Example 3: A runner starts at position x = 0 m and reaches position x = -50 m in 25 seconds.

Displacement = -50 m - 0 m = -50 m (negative indicates westward or backward direction)

Time = 25 s

Average Velocity = (-50 m) / (25 s) = -2 m/s (negative velocity, moving westward)

Position-Time Graphs

In a position-time graph, velocity is represented by the slope of the line:

A straight line represents constant velocity
A positive slope indicates positive velocity (moving in the positive direction)
A negative slope indicates negative velocity (moving in the negative direction)
A horizontal line (zero slope) indicates zero velocity (at rest)
A curved line indicates changing velocity (acceleration)

The average velocity between any two points on a position-time graph is the slope of the line connecting those points.

Common Velocity Unit Conversions

From	To	Multiply By
m/s	km/h	3.6
km/h	m/s	0.277778
m/s	mph	2.23694
mph	m/s	0.44704
km/h	mph	0.621371
mph	km/h	1.60934
m/s	ft/s	3.28084
ft/s	m/s	0.3048