Speed Formula

Q: What do the symbols mean in the Speed formula?

$s$ or $|v|$ is speed in m/s, 'distance' is the total path length in metres, and $\Delta t$ is the time interval in seconds. Speed is always non-negative.

The Formula

\text{speed} = \frac{\text{distance}}{\text{time}}

When to use: How fast you're going, ignoring which way—just the magnitude of motion.

Quick Example

A car's speedometer reads 60 mph whether turning left, right, or going straight.

Notation

s or |v| is speed in m/s, 'distance' is the total path length in metres, and \Delta t is the time interval in seconds. Speed is always non-negative.

What This Formula Means

The rate at which an object covers distance over time, calculated as total distance divided by total time, always expressed as a non-negative scalar quantity without direction.

How fast you're going, ignoring which way—just the magnitude of motion.

Formal View

Instantaneous speed is the magnitude of the velocity vector: |\vec{v}| = \sqrt{v_x^2 + v_y^2}. Average speed is \bar{s} = \frac{\text{total distance}}{\Delta t}, which is always \geq |\bar{v}|.

Worked Examples

Example 1

easy

A jogger runs 5 \text{ km} in 25 \text{ minutes}. What is the average speed in m/s?

Solution

1
Convert units: 5 \text{ km} = 5000 \text{ m} and 25 \text{ min} = 1500 \text{ s}.
2
Use the average speed formula: s = \frac{d}{t}.
3
Average speed: s = \frac{5000}{1500} \approx 3.33 \text{ m/s}

Answer

s \approx 3.33 \text{ m/s}

Speed is the rate at which distance is covered. Unlike velocity, speed is a scalar and does not include direction.

Example 2

medium

A train travels 120 \text{ km} at 60 \text{ km/h} and then 120 \text{ km} at 40 \text{ km/h}. What is the average speed for the whole trip?

Common Mistakes

Confusing speed with velocity — speed is a scalar (no direction), while velocity is a vector (includes direction).
Using displacement instead of total distance when calculating average speed — a round trip has nonzero average speed but zero average velocity.
Averaging speeds incorrectly — if you travel half the distance at 40 km/h and half at 60 km/h, the average speed is not 50 km/h but the harmonic mean.

Why This Formula Matters

Speed is the most intuitive measure of motion used in everyday life — from speed limits on roads to athletic performance. It provides a quick measure of how rapidly an object covers ground, regardless of direction.

Frequently Asked Questions

What is the Speed formula?

The rate at which an object covers distance over time, calculated as total distance divided by total time, always expressed as a non-negative scalar quantity without direction.