Distance Formula Physics: d = vt, Units and Solved Examples

The distance formula physics uses is $d = v \times t$ : multiply the speed by the time spent moving. A cyclist riding at 5 m/s for 60 s covers 300 m. If the speed changes during the trip, use the average speed for v and the formula still gives the total path length.

Do not confuse it with the distance formula from coordinate geometry, which finds the straight line gap between two points. In physics, distance is the total length of the path an object followed, bends and all. It is a scalar, measured in metres, and it can never be negative or decrease as time goes on.

Quick facts

Formula
$d = vt$
SI unit
metre (m)
Dimensional formula
[M⁰ L¹ T⁰]
Type
Scalar, always zero or positive
Constant acceleration, one direction
$d = ut + \frac{1}{2}at^2$
From a graph
Area under a speed time graph

Distance formula physics: each term explained

Quantities in d = v × t
Symbol	Quantity	SI unit
$d$	Distance travelled along the actual path	m
$v$	Speed, or average speed if it varies	m/s
$t$	Time spent moving	s

The formula is just the speed formula turned around. Speed tells you how many metres pass each second, so after t seconds the metres add up to v × t. The units confirm it: (m/s) × s = m.

What is the formula for distance in physics, and how do you use it?

Read the speed and the time from the question and note their units.
Make the units match: m/s with seconds, or km/h with hours.
Multiply. If the speed changes in stages, find the distance of each stage and add them.
Write the answer with its unit and ask whether the size is sensible.

The distance calculator above runs the same multiplication in SI units, and it can also solve backward for speed or time.

Worked examples

Example 1: a steady car

A car moves at a constant 25 m/s for 40 s. How far does it go?

$d = 25 \times 40 = 1000\ \text{m} = 1.0\ \text{km}$

Example 2: an express on rails, converting first

A train runs at 72 km/h for 15 minutes. Find the distance in metres.

Convert: 72 ÷ 3.6 = 20 m/s and 15 × 60 = 900 s.

$d = 20 \times 900 = 18\,000\ \text{m} = 18\ \text{km}$

Check in road units: $72 \times 0.25\ \text{h} = 18\ \text{km}$ .

Example 3: speeding up from rest

A scooter starts from rest and accelerates uniformly at 2.0 m/s² for 5.0 s in a straight line. Find the distance covered.

$d = ut + \tfrac{1}{2}at^2 = 0 + \tfrac{1}{2}(2.0)(5.0)^2 = 25\ \text{m}$

The scooter never turns back, so distance and displacement are both 25 m.

Distance when the speed is not constant

Real motion rarely runs at one speed, so physics has three ways to deal with it.

Stages. Split the trip into parts, each with its own speed. A bus that drives 10 min at 36 km/h and then 5 min at 54 km/h covers 6 km + 4.5 km = 10.5 km.

Uniform acceleration. When the speed changes at a steady rate in one direction, use $d = ut + \frac{1}{2}at^2$ or $d = \frac{(u + v)}{2} t$ . These come from the equations covered on the formula of motion page.

Graphs. On a speed time graph, distance is the area under the line. A rectangle gives speed times time, and a triangle gives half of base times height.

Distance versus displacement

Distance and displacement side by side
Feature	Distance	Displacement
What it measures	Length of the path	Straight line from start to finish
Type	Scalar	Vector
Can be zero after moving	No	Yes, on a round trip
Goes with	speed	velocity

Walk 40 m along a corridor and 40 m back: distance 80 m, displacement zero. The formula of displacement page shows how to find the straight line value. The path length can never come out smaller than the size of the displacement.

Common errors in distance problems

Unmatched units. km/h times minutes gives nonsense. Convert one of them.
Using displacement. If the path loops or reverses, add every leg as a positive length.
Dropping the half. Leaving the ½ off in ut + ½at² doubles the second term.
Negative answers. A distance cannot be negative. A minus sign means you were computing displacement.

Time and speed problems built on the same triangle sit together in the kinematics formulas section.

Frequently asked questions

What is the formula of distance in physics?

Distance = speed × time, or d = vt. If the object starts at speed u and accelerates uniformly in one direction, d = ut + ½at².

What is the SI unit of distance?

The metre (m). Kilometres and centimetres are also used, but convert to metres when you use SI formulas.

What is the distance formula for Class 9 physics?

Class 9 uses distance = speed × time for uniform motion and s = ut + ½at² for uniformly accelerated motion in a straight line.

Is distance a scalar or vector quantity?

Scalar. Distance tells you how much ground was covered with no direction attached, and it never shrinks while an object moves.

How is distance found from a graph?

Find the area under the speed time graph. For constant speed that area is a rectangle, speed × time.